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* prov-sem staging validity
authorjcheney@inf.ed.ac.uk
Thu, 04 Apr 2013 15:51:39 +0100
changeset 6048 57dcf1e0eb01
parent 6047 668b93ed1c7b
child 6049 e1fa26593295
* prov-sem staging validity
semantics/prov-sem.html
semantics/releases/NOTE-prov-sem-20130430/Overview.html 
--- a/semantics/prov-sem.html	Thu Apr 04 15:44:19 2013 +0100
+++ b/semantics/prov-sem.html	Thu Apr 04 15:51:39 2013 +0100
@@ -898,7 +898,7 @@
 };
       var respecConfig = {
           // specification status (e.g. WD, LCWD, NOTE, etc.). If in doubt use ED.
-          specStatus:           "ED",
+          specStatus:           "WG-NOTE",
           
           // the specification's short name, as in http://www.w3.org/TR/short-name/
           shortName:            "prov-sem",
@@ -910,7 +910,9 @@
 
 
           // if you wish the publication date to be other than today, set this
-          // publishDate:  "2013-04-30",
+           publishDate:  "2013-04-30",
+          previousPublishDate:  "2013-03-12",
+          previousMaturity:  "WD",
 
           // if the specification's copyright date is a range of years, specify
           // the start date here:
@@ -2431,8 +2433,6 @@
   = \rho(e_1) \in Entities$ and $ent_2 = \rho(e_2) \in Entities$.
 </li>
 <!--<li>$(ent_1,ent_2) \in SpecializationOf$.-->
-<ol>
-  <li>The two entities are different: $ent_1 \neq ent_2$.
   <li>The two entities present aspects of the same thing, that is, $thingOf(ent_1) = thingOf(ent_2)$.
 </li>
 <li>The lifetime of $ent_1$ is contained in that of $ent_2$, i.e. $lifetime(ent_1) \subseteq lifetime(ent_2)$.
@@ -3217,7 +3217,7 @@
 \end{array}$</div>
 
 <div class="proof">
-  <p>This follows from <a href="#axiom 23">Axiom 23</a>.
+  <p>This follows from <a href="#axiom23">Axiom 23</a>.
   </p>
   </div>
 
--- a/semantics/releases/NOTE-prov-sem-20130430/Overview.html	Thu Apr 04 15:44:19 2013 +0100
+++ b/semantics/releases/NOTE-prov-sem-20130430/Overview.html	Thu Apr 04 15:51:39 2013 +0100
@@ -774,7 +774,7 @@
 }
 
 
-</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-ED"><style type="text/css">DIV.MathJax_MathML {text-align: center; margin: .75em 0px}
+</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-WG-NOTE"><style type="text/css">DIV.MathJax_MathML {text-align: center; margin: .75em 0px}
 .MathJax_MathML {font-style: normal; font-weight: normal; line-height: normal; font-size: 100%; font-size-adjust: none; text-indent: 0; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; border: 0; padding: 0; margin: 0}
 span.MathJax_MathML {display: inline}
 div.MathJax_MathML {display: block}
@@ -788,11 +788,11 @@
   </p>
   <h1 class="title" id="title">Semantics of the PROV Data Model</h1>
   
-  <h2 id="w3c-editor-s-draft-04-april-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Editor's Draft 04 April 2013</h2>
+  <h2 id="w3c-working-group-note-30-april-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Working Group Note 30 April 2013</h2>
   <dl>
     
       <dt>This version:</dt>
-      <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
+      <dd><a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/</a></dd>
       <dt>Latest published version:</dt>
       <dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd>
     
@@ -803,8 +803,9 @@
     
     
     
-      
     
+      <dt>Previous version:</dt>
+      <dd><a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">http://www.w3.org/TR/2013/WD-prov-sem-20130312/</a></dd>
     
     
     <dt>Editor:</dt>
@@ -895,7 +896,7 @@
 
 
         <p>
-          This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as an Editor's Draft.
+          This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Working Group Note.
           
           
           If you wish to make comments regarding this document, please send them to 
@@ -910,7 +911,7 @@
         
         
           </p><p>
-            Publication as an Editor's Draft does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+            Publication as a Working Group Note does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
             This is a draft document and may be updated, replaced or obsoleted by other documents at 
             any time. It is inappropriate to cite this document as other than work in progress.
           </p>
@@ -2344,19 +2345,17 @@
   = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-546-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-546">ent_2 = \rho(e_2) \in Entities</script>.
 </li>
 <!--<li>$(ent_1,ent_2) \in SpecializationOf$.-->
-<ol>
-  <li>The two entities are different: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≠</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-547">ent_1 \neq ent_2</script>.
-  </li><li>The two entities present aspects of the same thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-548">thingOf(ent_1) = thingOf(ent_2)</script>.
+  <li>The two entities present aspects of the same thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-547">thingOf(ent_1) = thingOf(ent_2)</script>.
 </li>
-<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-549">ent_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-550">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-551">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-548">ent_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-549">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-550">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
 </li>
-<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-552">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-553">value(ent_1,attr) \supseteq value(ent_2,attr)</script>.</li>
+<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-551">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-552">value(ent_1,attr) \supseteq value(ent_2,attr)</script>.</li>
 <li>At least one of these inclusions is strict: that is, either
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊊</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-554">lifetime(ent_1) \subsetneq lifetime(ent_2)</script> or for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-555">attr</script> we
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊊</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-553">lifetime(ent_1) \subsetneq lifetime(ent_2)</script> or for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-554">attr</script> we
  value(ent_1,attr) \supsetneq value(ent_2,attr)$.
 </li>
 </ol>
-</ol></div>
+</div>
 
 <div class="remark">
   <!--<p>The conditions on the $SpecializationOf$ relation imply that:</p>
@@ -2370,10 +2369,10 @@
 </li></ol>
 -->
 <p>The second criterion says that the two Entities present (possibly different) aspects of
-the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-556">ent_1</script> and
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-557">ent_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-558">ent_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-559">ent_1</script> to have more defined attributes than
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-560">ent_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-561">ent_2</script>.  Two
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-555">ent_1</script> and
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-556">ent_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-557">ent_2</script> can be larger).
+The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-558">ent_1</script> to have more defined attributes than
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-559">ent_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-560">ent_2</script>.  Two
   different entities that have the same attributes can also be related
   by specialization.  
 </p>
@@ -2383,15 +2382,15 @@
 
 <h4><span class="secno">4.4.13 </span> Alternate </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-562">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_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-561">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="semantics" id="alternate-semantics" data-count="34" data-title="Semantics 34 (alternate-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#alternate-semantics">Semantics 34 (alternate-semantics)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-563">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-562">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-564">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-565">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-566">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-567">ent_2 = \rho(e_2)</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-563">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-564">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-565">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-566">ent_2 = \rho(e_2)</script>.
 </li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-568">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_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-567">thingOf(ent_1) = thingOf(ent_2)</script>
 </li></ol>
 </div>
 
@@ -2403,17 +2402,17 @@
 
 <h4><span class="secno">4.4.14 </span> Membership </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-569">hadMember</script> relation relates a collection to an element of the collection.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-568">hadMember</script> relation relates a collection to an element of the collection.
 </p>
 <div class="semantics" id="membership-semantics" data-count="35" data-title="Semantics 35 (membership-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#membership-semantics">Semantics 35 (membership-semantics)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-570">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-569">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-571">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-572">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-573">coll
-  = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-574">ent = \rho(e) \in Entities</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-570">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-571">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-572">coll
+  = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-573">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-575">ent</script> is a member of the collection <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-576">coll</script>: that is,
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-577">(ent,coll) \in MemberOf</script>.
+<li>The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-574">ent</script> is a member of the collection <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-575">coll</script>: that is,
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-576">(ent,coll) \in MemberOf</script>.
 </li></ol>
 </div>
 
@@ -2432,20 +2431,20 @@
   
   <section id="precedes-and-strictly-precedes">
   <h4><span class="secno">4.5.1 </span>Precedes and Strictly Precedes</h4>
-  <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-578">x \precedes y</script> holds between two events, one taking
+  <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-577">x \precedes y</script> holds between two events, one taking
   place before (or simultaneously with) another.  Its meaning is
   defined in terms of the quasiordering on events specified by
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-579">\preceq</script>.  The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-580">x
-  \strictlyPrecedes y</script>) is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-581">x</script> must take place strictly
-  before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-582">y</script>.  It is interpreted as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≺</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-583">\prec</script>, which we recall is
-  defined from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-584">\preceq</script> as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi><mtext>&nbsp;and&nbsp;</mtext><mi>y</mi><mo stretchy="false">⪯̸</mo><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">x \prec y \iff x \preceq y \text{ and } y
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-578">\preceq</script>.  The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-579">x
+  \strictlyPrecedes y</script>) is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-580">x</script> must take place strictly
+  before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-581">y</script>.  It is interpreted as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≺</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-582">\prec</script>, which we recall is
+  defined from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-583">\preceq</script> as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi><mtext>&nbsp;and&nbsp;</mtext><mi>y</mi><mo stretchy="false">⪯̸</mo><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-584">x \prec y \iff x \preceq y \text{ and } y
   \not\preceq x</script>.</p>
   <div class="semantics" id="precedes-semantics" data-count="36" data-title="Semantics 36 (precedes-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#precedes-semantics">Semantics 36 (precedes-semantics)</a></div>
     <ol>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-586">W,\rho \models x \precedes y</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-587">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⪯</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-588">\rho(x) \preceq\rho(y)</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-589">W,\rho \models x \strictlyPrecedes y</script> holds if and only if
-       <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-590">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">≺</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-591">\rho(x) \prec \rho(y)</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">W,\rho \models x \precedes y</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-586">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⪯</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-587">\rho(x) \preceq\rho(y)</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-588">W,\rho \models x \strictlyPrecedes y</script> holds if and only if
+       <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-589">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">≺</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-590">\rho(x) \prec \rho(y)</script>.</li>
     </ol>
   </div>
 
@@ -2459,7 +2458,7 @@
 wasGeneratedBy(gen2; e, a2, 2012-11-16T16:05:00) //different date
 </pre>
     <p>This instance is valid, and must satisfy precedence constraints
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-592">gen_1 \precedes gen_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-593">gen_2 \precedes gen_1</script>, but this does not
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-591">gen_1 \precedes gen_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-592">gen_2 \precedes gen_1</script>, but this does not
     imply anything about the relative orderings of the associated
     times, or vice versa.
     </p>
@@ -2469,11 +2468,11 @@
   
   <section id="notnull">
   <h4><span class="secno">4.5.2 </span>notNull</h4>
-  <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-594">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_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-595">\bot</script>.  The symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-596">-</script> always denotes the null
-  value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-597">\rho(-) = \bot</script>).
+  <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-593">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_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-594">\bot</script>.  The symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-595">-</script> always denotes the null
+  value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-596">\rho(-) = \bot</script>).
   </p><div class="semantics" id="notNull-semantics" data-count="37" data-title="Semantics 37 (notNull-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#notNull-semantics">Semantics 37 (notNull-semantics)</a></div>
-    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-598">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-599">\rho(e) \neq
+    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-597">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-598">\rho(e) \neq
   \bot</script>.
       </p>
   </div> 
@@ -2483,21 +2482,21 @@
   <section id="typeof">
   <h4><span class="secno">4.5.3 </span>typeOf</h4>
   
-  <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-600">typeOf(x,t)</script> constrains the type of the value of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-601">x</script>.  </p>
+  <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-599">typeOf(x,t)</script> constrains the type of the value of
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-600">x</script>.  </p>
 
   <div class="semantics" id="typeOf-semantics" data-count="38" data-title="Semantics 38 (typeOf-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#typeOf-semantics">Semantics 38 (typeOf-semantics)</a></div>
-    <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-602">W,\rho\models typeOf(e,entity)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-603">\rho(e) \in Entities</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-604">W,\rho\models typeOf(a,activity)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-605">\rho(a) \in Activities</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-606">W,\rho\models typeOf(ag,agent)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-607">\rho(ag) \in Agents</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-608">W,\rho\models typeOf(c,Collection)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-609">\rho(c) \in Collections</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-610">W,\rho\models typeOf(c,EmptyCollection)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-611">\rho(c) \in Collections</script> and there is no <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-612">e \in Entities</script> such
-    that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-613">(e,\rho(c)) \in MemberOf</script>.</li>
+    <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-601">W,\rho\models typeOf(e,entity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-602">\rho(e) \in Entities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-603">W,\rho\models typeOf(a,activity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-604">\rho(a) \in Activities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-605">W,\rho\models typeOf(ag,agent)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-606">\rho(ag) \in Agents</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-607">W,\rho\models typeOf(c,Collection)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-608">\rho(c) \in Collections</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-609">W,\rho\models typeOf(c,EmptyCollection)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-610">\rho(c) \in Collections</script> and there is no <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-611">e \in Entities</script> such
+    that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-612">(e,\rho(c)) \in MemberOf</script>.</li>
       </ol>
       
     </div>
@@ -2521,7 +2520,7 @@
 <section id="inferences">
 <h3><span class="secno">5.1 </span>Inferences</h3>
 
-<div class="inference" 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_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-614">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-613">\begin{array}[t]{l}
 \forall id,a_2,a_1,attrs.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs)
@@ -2531,9 +2530,9 @@
 \end{array}</script></div>
 
 <div class="proof">
-<p> This follows immediately from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-615">wasInformedBy</script>.</p>
+<p> This follows immediately from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-614">wasInformedBy</script>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-616">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-615">\begin{array}[t]{l}
 \forall gen,e,a_1,t_1,attrs_1,use,a_2,t_2,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
@@ -2542,9 +2541,9 @@
 \exists id.~wasInformedBy(id,a_2,a_1,[])
 \end{array}</script></div>
 <div class="proof">
-<p> This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-617">wasInformedBy</script> and <a href="#axiom1">Axiom 1</a>.</p>
+<p> This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-616">wasInformedBy</script> and <a href="#axiom1">Axiom 1</a>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-618">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-617">\begin{array}[t]{l}
 \forall e,attrs.~
 \\
 \qquad entity(e,attrs)
@@ -2558,7 +2557,7 @@
   the requirement that generation and invalidation events exist for
   the entity.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-619">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-618">\begin{array}[t]{l}
 \forall a,t_1,t_2,attrs.~
 \\
 \qquad activity(a,t_1,t_2,attrs)
@@ -2574,7 +2573,7 @@
   </div>
 
   
-<div class="inference" 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_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-620">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-619">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
@@ -2586,7 +2585,7 @@
 <div class="proof">
   <p>This follows from <a href="#axiom2">Axiom 2</a>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-621">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-620">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
@@ -2599,7 +2598,7 @@
   <p>This follows from <a href="#axiom3">Axiom 3</a>.</p>
   </div>
 <div class="inference" id="derivation-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-use-inference">Inference 11 (derivation-generation-use-inference)</a></div>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-622">\begin{array}[t]{l}
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-621">\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)
@@ -2613,7 +2612,7 @@
   </div>
   
 <div class="inference" id="revision-is-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#revision-is-alternate-inference">Inference 12 (revision-is-alternate-inference)</a></div>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-623">\begin{array}[t]{l}
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-622">\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]))
@@ -2625,7 +2624,7 @@
   <p> This follows from the semantics of derivation steps (precise or
   imprecise) and <a href="#axiom4">Axiom 4</a>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-624">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-623">\begin{array}[t]{l}
 \forall att,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(att,e,ag,attrs)
@@ -2638,7 +2637,7 @@
   attribution, by <a href="#axiom5">Axiom 5</a></p>
   </div>
   
-<div class="inference" 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_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-625">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-624">\begin{array}[t]{l}
 \forall id,ag_1,ag_2,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
@@ -2649,49 +2648,49 @@
 <div class="proof">
   <p>This follows from the semantics of association and delegation, by <a href="#axiom6">Axiom 6</a></p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-626">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-625">\begin{array}[t]{l}
 \forall id,e,a,t,attrs.~
 \\
 \qquad wasGeneratedBy(id,e,a,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-627">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-626">\begin{array}[t]{l}
 \forall id,a,e,t,attrs.~
 \\
 \qquad used(id,a,e,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-628">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-627">\begin{array}[t]{l}
 \forall id,a_2,a_1,attrs.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,a_1,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-628">\begin{array}[t]{l}
 \forall id,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(id,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-630">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
 \forall id,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(id,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-631">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-630">\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}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-632">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-631">\begin{array}[t]{l}
 \forall id,e_2,e_1,a,g,u,attrs.~
 \\
 \qquad wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)
@@ -2699,7 +2698,7 @@
 \quad\Rightarrow
 wasInfluencedBy(id,e_2,e_1,attrs)
 \end{array}</script></li><li>
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-633">\begin{array}[t]{l}
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-632">\begin{array}[t]{l}
 \forall id,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(id,e,ag,attrs)
@@ -2707,14 +2706,14 @@
 \quad\Rightarrow
 wasInfluencedBy(id,e,ag,attrs)
 \end{array}</script></li><li>
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-634">\begin{array}[t]{l}
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-633">\begin{array}[t]{l}
 \forall id,a,ag,pl,attrs.~
 \\
 \qquad wasAssociatedWith(id,a,ag,pl,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a,ag,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-635">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-634">\begin{array}[t]{l}
 \forall id,ag_2,ag_1,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
@@ -2726,7 +2725,7 @@
 <div class="proof">
   <p>This follows via <a href="#axiom7">Axioms 7</a> through <a href="#axiom16">16</a>.
   </p></div>
-<div class="inference" 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_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-636">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-635">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad entity(e)
@@ -2735,10 +2734,10 @@
 alternateOf(e,e)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-637">ent = \rho(e)</script>.  Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-638">ent \in Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-639">thingOf(ent) = thingOf(ent)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-640">W,\rho \models alternateOf(e,e)</script>.</p>
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-636">ent = \rho(e)</script>.  Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-637">ent \in Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-638">thingOf(ent) = thingOf(ent)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-639">W,\rho \models alternateOf(e,e)</script>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-641">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-640">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
@@ -2747,13 +2746,13 @@
 alternateOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-642">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-643">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-644">ent_3 = \rho(e_3)</script>.  Then  by
-  assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-645">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-646">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-647">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-648">Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-649">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-650">thingOf(e_2) = thingOf(e_3)</script>, so
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-651">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-652">W,\rho
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-641">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-642">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-643">ent_3 = \rho(e_3)</script>.  Then  by
+  assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-644">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-645">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-646">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-647">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-648">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-649">thingOf(e_2) = thingOf(e_3)</script>, so
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-650">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-651">W,\rho
   \models alternateOf(e_1,e_3)</script>.</p>
   </div>
-<div class="inference" 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_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-653">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-652">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad alternateOf(e_1,e_2)
@@ -2762,13 +2761,13 @@
 alternateOf(e_2,e_1)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-654">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-655">ent_2 = \rho(e_2)</script>.  Then  by
-  assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-656">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-657">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-658">Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-659">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-660">W,\rho
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-653">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-654">ent_2 = \rho(e_2)</script>.  Then  by
+  assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-655">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-656">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-657">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-658">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-659">W,\rho
   \models alternateOf(e_2,e_1)</script>.</p>
   </div>
   
-<div class="inference" 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_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-661">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-660">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
@@ -2777,20 +2776,20 @@
 specializationOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-662">ent_1</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-663">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-664">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-665">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-666">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-667-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-667">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-668-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-668">ent_3 =
-  \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-669-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-669">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
+  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-661">ent_1</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-662">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-663">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-664">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-665">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-666">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-667-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-667">ent_3 =
+  \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-668-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-668">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
   lifetime(e_3)</script>.  Moreover, 
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-670-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-670">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-671-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-671">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-672-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-672">value(obj_1,attr)
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-669-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-669">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-670-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-670">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-671-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-671">value(obj_1,attr)
   \supseteq value(obj_3,attr)</script>.  Finally, at least one of the
-  inclusions between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-673-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-673">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-674-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-674">obj_2</script> is strict, so the same is the
-  case for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-675-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-675">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-676-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-676">obj_3</script>.
+  inclusions between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-672-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-672">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-673-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-673">obj_2</script> is strict, so the same is the
+  case for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-674-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-674">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-675-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-675">obj_3</script>.
 </p>
 </div>
 
 
-<div class="inference" 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_MathML" id="MathJax-Element-677-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-677">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-676-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-676">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad specializationOf(e_1,e_2)
@@ -2799,12 +2798,12 @@
 alternateOf(e_1,e_2)
 \end{array}</script></div>
 <div class="proof">
-  <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-678-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-678">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-679-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-679">ent_2 = \rho(e_2)</script> are
-  specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-680-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-680">thingOf(ent_1) = thingOf(ent_2)</script>.
+  <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-677-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-677">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-678-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-678">ent_2 = \rho(e_2)</script> are
+  specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-679-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-679">thingOf(ent_1) = thingOf(ent_2)</script>.
 </p>
 </div>
 
-<div class="inference" 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_MathML" id="MathJax-Element-681-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-681">\begin{array}[t]{l}
+<div class="inference" 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_MathML" id="MathJax-Element-680-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-680">\begin{array}[t]{l}
 \forall e_1,attrs,e_2.~
 \\
 \qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
@@ -2814,12 +2813,12 @@
 \end{array}</script></div>
 </section>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-682-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-682">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-683-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-683">ent_2 = \rho(e_2)</script>.  Suppose
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-684-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-684">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-685-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-685">attrs</script>.  Since
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-686-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-686">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-687-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-687">v \in value(ent_1,att)</script>.
-  Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-688-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-688">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-689-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-689">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_MathML" id="MathJax-Element-690-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-690">attrs</script>, and since
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-691-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-691">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-692-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-692">W,\rho \models entity(e,attrs</script>).
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-681-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-681">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-682-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-682">ent_2 = \rho(e_2)</script>.  Suppose
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-683-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-683">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-684-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-684">attrs</script>.  Since
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-685-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-685">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-686-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-686">v \in value(ent_1,att)</script>.
+  Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-687-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-687">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-688-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-688">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_MathML" id="MathJax-Element-689-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-689">attrs</script>, and since
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-690-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-690">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-691-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-691">W,\rho \models entity(e,attrs</script>).
   </p>
 </div>
 
@@ -2829,14 +2828,14 @@
 <h4><span class="secno">5.2.1 </span>Uniqueness constraints</h4>
 
 <div class="constraint" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint 22 (key-object)</a></div>
-  <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-693-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-693">\forall
+  <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-692-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-692">\forall
   id,attrs_1,attrs_2. entity(id,attrs_1) \wedge entity(id,attrs_2)
   \Rightarrow entity(id,attrs_1\cup attrs_2)</script></li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-694-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-694">\forall
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-693-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-693">\forall
   id,t_1,t_1',t_2,t_2',attrs_1,attrs_2.~ activity(id,t_1,t_2,attrs_1)
   \wedge activity(id,t_1',t_2',attrs_2) \Rightarrow
   activity(id,t_1,t_2,attrs_1\cup attrs_2) \wedge t_1=t_1' \wedge t_2=t_2'</script></li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-695-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-695">\forall
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-694-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-694">\forall
   id,attrs_1,attrs_2. agent(id,attrs_1) \wedge agent(id,attrs_2)
   \Rightarrow agent(id,attrs_1\cup attrs_2)</script>.</li></ol></div>
   <div class="proof">
@@ -2845,7 +2844,7 @@
   for the underlying data.</p>
     </div>
 <div class="constraint" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint 23 (key-properties)</a></div>
-  <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-696-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-696">\begin{array}[t]{l}
+  <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-695-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-695">\begin{array}[t]{l}
     \forall
   id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\
     wasGeneratedBy(id,e,a,t,attrs)
@@ -2853,61 +2852,61 @@
     \quad \Rightarrow
   wasGeneratedBy(id,e,a,t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
   a=a' \wedge t = t'\end{array}</script></li>
-    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-697-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-697">\begin{array}[t]{l}\forall
+    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-696-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-696">\begin{array}[t]{l}\forall
   id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\used(id,a,e,t,attrs)
   \wedge used(id,a',e',t',attrs_2)\\ \quad \Rightarrow
   used(id,a,e',t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
   a=a' \wedge t = t'
     \end{array}</script></li>
-    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-698-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-698">\begin{array}[t]{l}\forall
+    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-697-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-697">\begin{array}[t]{l}\forall
   id,a_1,a_2,a_1',a_2',attrs_1,attrs_2.~ \\wasInformedBy(id,a_1,a_2,attrs)
   \wedge wasInformedBy(id,a_1',a_2',attrs_2)\\ \Rightarrow
   wasInformedBy(id,a_1,a_2,attrs_1 \cup attrs_2) \wedge a_1=a_1'
   \wedge a_2=a_2'
     \end{array}</script></li>
-    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-699-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-699">\begin{array}[t]{l}\forall
+    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-698-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-698">\begin{array}[t]{l}\forall
   id,e,e'a_1,a_2,a_1',a_2',t,t',attrs_1,attrs_2.~ \\wasStartedBy(id,a_2,e,a_1,t,attrs_1)
   \wedge wasStartedBy(id,a_2',e',a_1',t',attrs_2)\\ \Rightarrow
   wasStartedBy(id,a_2,e,a_1,t,attrs_1 \cup attrs_2) \wedge a_1=a_1'
   \wedge e=e' \wedge
   a_2=a_2' \wedge t = t'
     \end{array}</script></li>
-    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-700-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-700">\begin{array}[t]{l}\forall
+    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-699-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-699">\begin{array}[t]{l}\forall
   id,e,e'a_1,a_2,a_1',a_2',t,t',attrs_1,attrs_2.~ \\wasEndedBy(id,a_2,e,a_1,t,attrs_1)
   \wedge wasEndedBy(id,a_2',e',a_1',t',attrs_2)\\ \Rightarrow
   wasEndedBy(id,a_2,e,a_1,t,attrs_1 \cup attrs_2) \wedge a_1=a_1'
   \wedge e=e' \wedge
   a_2=a_2' \wedge t = t'
     \end{array}</script></li>
-    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-701-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-701">\begin{array}[t]{l}\forall
+    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-700-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-700">\begin{array}[t]{l}\forall
   id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\wasInvalidatedBy(id,e,a,t,attrs_1)
   \wedge wasInvalidatedBy(id,e',a',t',attrs_2)\\ \Rightarrow
   wasInvalidatedBy(id,e,a,t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
   a=a' \wedge t = t'
     \end{array}</script></li>
-    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-702-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msup><mi>u</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>u</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>g</mi><mo stretchy="false">=</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>u</mi><mo stretchy="false">=</mo><msup><mi>u</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-702">\begin{array}[t]{l}\forall
+    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-701-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msup><mi>u</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>u</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>g</mi><mo stretchy="false">=</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>u</mi><mo stretchy="false">=</mo><msup><mi>u</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-701">\begin{array}[t]{l}\forall
   id,e_1,e_1',e_2,e_2',a,a',g,g',u,u',attrs_1,attrs_2.~ \\wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs_1)
   \wedge wasDerivedFrom(id,e_2',e_1',a',g_2',u_1',attrs_2)\\ \Rightarrow
   wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs_1 \cup attrs_2) \wedge e_1=e_1'\wedge e_2=e_2'\wedge a=a'\wedge g=g'\wedge u=u'
     \end{array}</script></li>
-    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-703-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-703">\begin{array}[t]{l}\forall
+    <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-702-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-702">\begin{array}[t]{l}\forall
   id,e,e',ag,ag',attrs_1,attrs_2.~ \\wasAttributedTo(id,e,ag,attrs_1)
   \wedge wasAttributedTo(id,e',ag',attrs_2)\\ \Rightarrow
   wasAttributedTo(id,e,ag,attrs_1 \cup attrs_2) \wedge e=e' \wedge ag = ag'
     \end{array}</script></li>
-    <li> <br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-704-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>p</mi><mi>l</mi><mo stretchy="false">=</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-704">\begin{array}[t]{l}\forall
+    <li> <br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-703-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>p</mi><mi>l</mi><mo stretchy="false">=</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-703">\begin{array}[t]{l}\forall
   id,a,a',ag,ag',pl,pl',attrs_1,attrs_2.~ \\wasAssociatedWith(id,a,ag,pl,attrs_1)
   \wedge wasAssociatedWith(id,a',ag',pl',attrs_2)\\ \Rightarrow
   wasAssociatedWith(id,a,ag,pl,attrs_1 \cup attrs_2) \wedge a=a'
   \wedge ag=ag'   \wedge pl=pl'
     \end{array}</script></li>
-    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-705-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-705">\begin{array}[t]{l}\forall
+    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-704-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-704">\begin{array}[t]{l}\forall
   id,ag_1,ag_1',ag_2,ag_2',a,a',attrs_1,attrs_2.~ \\actedOnBehalfOf(id,ag_2,ag_1,a,attrs_1)
   \wedge actedOnBehalfOf(id,ag_2',ag_1',a',attrs_2)\\ \Rightarrow
   actedOnBehalfOf(id,ag_2,ag_1,a,attrs_1 \cup attrs_2) \wedge
   ag_1=ag_1' \wedge ag_2 = ag_2' \wedge a = a'
     \end{array}</script></li>
-    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-706-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-706">\begin{array}[t]{l}\forall
+    <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-705-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-705">\begin{array}[t]{l}\forall
   id,o_1,o_2,o_1',o_2',attrs_1,attrs_2.~ \\wasInfluencedBy(id,o_2',o_1',attrs_1)
   \wedge wasInfluencedBy(id,o_2',o_1',attrs_2)\\ \Rightarrow
   wasInfluencedBy(id,o_2,o_1,attrs_1 \cup attrs_2) \wedge o_1=o_1'
@@ -2919,7 +2918,7 @@
   semantics of the respective assertions, again because functions are
   used for the underlying data.</p>
     </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-707-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-707">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-706-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-706">\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)
@@ -2932,7 +2931,7 @@
   This follows from <a href="#axiom17">Axiom 17</a>.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-708-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-708">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-707-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-707">\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)
@@ -2945,7 +2944,7 @@
   This follows from <a href="#axiom17">Axiom 18</a>.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-709-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-709">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-708-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-708">\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)
@@ -2959,7 +2958,7 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-710-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-710">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-709-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-709">\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)
@@ -2972,7 +2971,7 @@
   This follows from <a href="#axiom17">Axiom 20</a>.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-711-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-711">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-710-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-710">\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)
@@ -2982,11 +2981,11 @@
 \end{array}</script></div>
 <div class="proof">
   <p>
-  This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-712-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-712">wasStartedBy</script>, since the start times
+  This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-711-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-711">wasStartedBy</script>, since the start times
   must both match that of the activity.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-713-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-713">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-712-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-712">\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)
@@ -2996,7 +2995,7 @@
 \end{array}</script></div>
 <div class="proof">
   <p>
-  This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-714-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-714">wasEndedBy</script>, since the end times
+  This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-713-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-713">wasEndedBy</script>, since the end times
   must both match that of the activity.
   </p>
   </div>
@@ -3006,7 +3005,7 @@
 <h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
 
 
-<div class="constraint" 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_MathML" id="MathJax-Element-715-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-715">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-714-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-714">\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)
@@ -3019,7 +3018,7 @@
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-716-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-716">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-715-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-715">\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)
@@ -3032,7 +3031,7 @@
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-717-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-717">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-716-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-716">\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)
@@ -3045,14 +3044,14 @@
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-718-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-718">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-717-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-717">\begin{array}[t]{l}
 \forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge used(use,a,e_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 start \precedes use
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-719-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-719">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-718-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-718">\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)
@@ -3066,14 +3065,14 @@
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-720-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-720">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-719-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-719">\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 \precedes gen
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-721-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-721">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-720-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-720">\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)
@@ -3087,7 +3086,7 @@
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-722-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-722">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-721-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-721">\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)
@@ -3096,14 +3095,14 @@
 start \precedes end
 \end{array}</script></div>
 <div class="proof">
-  <p>This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-723-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-723">wasInformedBy</script> and the
-  previous two constraints, because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-724-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-724">wasInformedBy</script> implies the
-  existence of intermediate generation and usage events linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-725-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-725">a_1</script>
-  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-726-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-726">a_2</script>.
+  <p>This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-722-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-722">wasInformedBy</script> and the
+  previous two constraints, because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-723-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-723">wasInformedBy</script> implies the
+  existence of intermediate generation and usage events linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-724-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-724">a_1</script>
+  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-725-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-725">a_2</script>.
   </p>
   </div>
   
-<div class="constraint" 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_MathML" id="MathJax-Element-727-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-727">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-726-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-726">\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)
@@ -3117,7 +3116,7 @@
   </p>
   </div>
 
-  <div class="constraint" 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_MathML" id="MathJax-Element-728-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-728">\begin{array}[t]{l}
+  <div class="constraint" 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_MathML" id="MathJax-Element-727-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-727">\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)
@@ -3127,11 +3126,11 @@
 \end{array}</script></div>
 
 <div class="proof">
-  <p>This follows from <a href="#axiom 23">Axiom 23</a>.
+  <p>This follows from <a href="#axiom23">Axiom 23</a>.
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-729-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-729">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-728-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-728">\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)
@@ -3145,7 +3144,7 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-730-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-730">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-729-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-729">\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)
@@ -3159,7 +3158,7 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-731-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-731">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-730-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-730">\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)
@@ -3173,7 +3172,7 @@
   </p>
   </div>
 
-<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-732-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-732">\begin{array}[t]{l}
+<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-731-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-731">\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)
@@ -3187,7 +3186,7 @@
   </p>
   </div>
 
-<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-733-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-733">\begin{array}[t]{l}
+<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-732-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-732">\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)
@@ -3201,14 +3200,14 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-734-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-734">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-733-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-733">\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 \precedes start
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-735-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-735">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-734-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-734">\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)
@@ -3223,14 +3222,14 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-736-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-736">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-735-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-735">\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 \precedes end
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-737-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-737">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-736-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-736">\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)
@@ -3245,7 +3244,7 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-738-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-738">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-737-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-737">\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)
@@ -3260,7 +3259,7 @@
   </p>
   </div>
 
-  <div class="constraint" 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_MathML" id="MathJax-Element-739-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-739">\begin{array}[t]{l}
+  <div class="constraint" 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_MathML" id="MathJax-Element-738-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-738">\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)
@@ -3274,28 +3273,28 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-740-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-740">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-741-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-741">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-739-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-739">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-740-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-740">\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 \precedes inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-742-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-742">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-741-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-741">\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 \precedes end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-743-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-743">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-742-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-742">\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 \precedes end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-744-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-744">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-743-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-743">\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)
@@ -3309,14 +3308,14 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-745-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-745">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-744-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-744">\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 \precedes gen_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-746-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-746">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-745-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-745">\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)
@@ -3330,14 +3329,14 @@
   </p>
   </div>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-747-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-747">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-746-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-746">\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 \precedes inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-748-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-748">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-747-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext>&nbsp;</mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext>&nbsp;</mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-747">\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)
@@ -3357,133 +3356,133 @@
 <section id="typing-constraints">
 <h4><span class="secno">5.2.3 </span>Typing constraints</h4>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-749-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-749">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-748-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-748">\begin{array}[t]{l}
 \forall e,attrs.~
 \\
 \qquad entity(e,attrs)
 \\
 \quad\Rightarrow
 typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-750-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-750">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-749-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-749">\begin{array}[t]{l}
 \forall ag,attrs.~
 \\
 \qquad agent(ag,attrs)
 \\
 \quad\Rightarrow
 typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-751-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-751">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-750-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-750">\begin{array}[t]{l}
 \forall a,t_1,t_2,attrs.~
 \\
 \qquad activity(a,t_1,t_2,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-752-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-752">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-751-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-751">\begin{array}[t]{l}
 \forall u,a,e,t,attrs.~
 \\
 \qquad used(u,a,e,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-753-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-753">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-752-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-752">\begin{array}[t]{l}
 \forall g,a,e,t,attrs.~
 \\
 \qquad wasGeneratedBy(g,e,a,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-754-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-754">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-753-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-753">\begin{array}[t]{l}
 \forall inf,a_2,a_1,t,attrs.~
 \\
 \qquad wasInformedBy(inf,a_2,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-755-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-755">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-754-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-754">\begin{array}[t]{l}
 \forall start,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-756-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-756">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-755-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-755">\begin{array}[t]{l}
 \forall end,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(end,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-757-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-757">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-756-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-756">\begin{array}[t]{l}
 \forall inv,a,e,t,attrs.~
 \\
 \qquad wasInvalidatedBy(inv,e,a,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-758-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-758">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-757-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-757">\begin{array}[t]{l}
 \forall id,e_2,e_1,a,g_2,u_1,attrs.~
 \\
 \qquad notNull(a) \wedge notNull(g_2) \wedge notNull(u_1) \wedge wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,activity) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-759-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-759">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-758-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-758">\begin{array}[t]{l}
 \forall id,e_2,e_1,attrs.~
 \\
 \qquad wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-760-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-760">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-759-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-759">\begin{array}[t]{l}
 \forall id,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(id,e,ag,attrs)
 \\
 \quad\Rightarrow
 typeOf(e,entity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-761-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-761">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-760-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-760">\begin{array}[t]{l}
 \forall id,a,ag,pl,attrs.~
 \\
 \qquad notNull(pl) \wedge wasAssociatedWith(id,a,ag,pl,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(ag,agent) \wedge typeOf(pl,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-762-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-762">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-761-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-761">\begin{array}[t]{l}
 \forall id,a,ag,attrs.~
 \\
 \qquad wasAssociatedWith(id,a,ag,-,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-763-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-763">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-762-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-762">\begin{array}[t]{l}
 \forall id,ag_2,ag_1,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
 \\
 \quad\Rightarrow
 typeOf(ag_2,agent) \wedge typeOf(ag_1,agent) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-764-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-764">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-763-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-763">\begin{array}[t]{l}
 \forall e_2,e_1.~
 \\
 \qquad alternateOf(e_2,e_1)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-765-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-765">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-764-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-764">\begin{array}[t]{l}
 \forall e_2,e_1.~
 \\
 \qquad specializationOf(e_2,e_1)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-766-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-766">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-765-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-765">\begin{array}[t]{l}
 \forall c,e.~
 \\
 \qquad hadMember(c,e)
 \\
 \quad\Rightarrow
 typeOf(c,Collection) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-767-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-767">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-766-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-766">\begin{array}[t]{l}
 \forall c.~
 \\
 \qquad entity(c,[prov:type = prov:emptyCollection]))
@@ -3501,21 +3500,21 @@
 <section id="impossibility-constraints">
 <h4><span class="secno">5.2.4 </span>Impossibility constraints</h4>
 
-<div class="constraint" 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_MathML" id="MathJax-Element-768-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-768">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-767-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-767">\begin{array}[t]{l}
 \forall id,e_1,e_2,g,attrs.~
 \\
 \qquad notNull(g) \wedge wasDerivedFrom(id,e_2,e_1,-,g,-,attrs)
 \\
 \quad\Rightarrow
 False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-769-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-769">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-768-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-768">\begin{array}[t]{l}
 \forall id,e_1,e_2,u,attrs.~
 \\
 \qquad notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,-,u,attrs)
 \\
 \quad\Rightarrow
 False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-770-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-770">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-769-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-769">\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)
@@ -3525,10 +3524,10 @@
 \end{array}</script></li></ol></div>
 <div class="proof">
   <p>Each part follows from the fact that the semantics of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-771-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-771">wasDerivedFrom</script> only allows formulas to hold when either all three
-  of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-772-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-772">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-773-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-773">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-774-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-774">\bot</script>) or none of them are.</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-770-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-770">wasDerivedFrom</script> only allows formulas to hold when either all three
+  of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-771-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-771">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-772-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-772">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-773-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-773">\bot</script>) or none of them are.</p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-775-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-775">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-774-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-774">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad specializationOf(e,e)
@@ -3538,11 +3537,11 @@
 \end{array}</script></div>
 <div class="proof">
   <p>This follows from the fact that in the semantics of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-776-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-776">specializationOf</script>, the two entities denoted by the first and second
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-775-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-775">specializationOf</script>, the two entities denoted by the first and second
   arguments are required to be distinct.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-777-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-777">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-778-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-778">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-779-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-779">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-780-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-780">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-781-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-781">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-776-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-776">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-777-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-777">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-778-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-778">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-779-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-779">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-780-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-780">\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)
@@ -3555,7 +3554,7 @@
   influences are disjoint sets, characterized by their types.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-782-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-782">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-783-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-783">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_MathML" id="MathJax-Element-784-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-784">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-781-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-781">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-782-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-782">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_MathML" id="MathJax-Element-783-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-783">\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)
@@ -3568,7 +3567,7 @@
   from other objects (entities, activities or agents).
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-785-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-785">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-784-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-784">\begin{array}[t]{l}
 \forall id.~
 \\
 \qquad typeOf(id,entity) \wedge typeOf(id,activity)
@@ -3580,7 +3579,7 @@
   <p>This follows from the assumption that entities and activities are disjoint.
   </p>
   </div>
-<div class="constraint" 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_MathML" id="MathJax-Element-786-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-786">\begin{array}[t]{l}
+<div class="constraint" 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_MathML" id="MathJax-Element-785-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-785">\begin{array}[t]{l}
 \forall c,e.~
 \\
 \qquad hasMember(c,e) \wedge typeOf(c,EmptyCollection)
@@ -3590,8 +3589,8 @@
 \end{array}</script></div>
 <div class="proof">
   <p>This follows from the definition of the semantics of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-787-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-787">typeOf(c,EmptyCollection)</script>, which requires that there are no
-  members of the collection denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-788-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-788">c</script>.
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-786-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-786">typeOf(c,EmptyCollection)</script>, which requires that there are no
+  members of the collection denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-787-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-787">c</script>.
   </p>
   </div>
 </section>
@@ -3614,33 +3613,33 @@
 <p>Our main soundness result is:</p>
 
 <div class="theorem" id="soundness-theorem" data-count="39" data-title="Theorem 39 (soundness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#soundness-theorem">Theorem 39 (soundness-theorem)</a></div>
-  <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-789-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-789">W</script> be a PROV model, that is, a structure satisfying all of
+  <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-788-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-788">W</script> be a PROV model, that is, a structure satisfying all of
   the axioms</p>.
   <ol>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-790-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-790">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-791-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-791">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-792-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-792">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-793-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-793">I</script> by applying one
-  of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-794-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-794">W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-795-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-795">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-796-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-796">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-797-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-797">I</script> has a normal
-  form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-798-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-798">I'</script> and   <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-799-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-799"> W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-800-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-800">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-801-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-801">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-802-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-802">I</script> satisfies all of the ordering,
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-789-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-789">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-790-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-790">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-791-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-791">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-792-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-792">I</script> by applying one
+  of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-793-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-793">W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-794-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-794">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-795-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-795">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-796-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-796">I</script> has a normal
+  form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-797-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-797">I'</script> and   <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-798-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-798"> W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-799-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-799">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-800-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-800">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-801-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-801">I</script> satisfies all of the ordering,
   typing and impossibility constraints.
-  </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-803-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-803">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-804-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-804">I</script> is valid.</li>
+  </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-802-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-802">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-803-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-803">I</script> is valid.</li>
 </ol>
   </div>
 <div class="proof">
   <p>For part 1, the arguments are as in the previous section.  </p>
   <p>For
   part 2, proceed by induction on a terminating sequence of inference
-  or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-805-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-805">I</script> is in normal form then we are
-  done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-806-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-806">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_MathML" id="MathJax-Element-807-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-807">W \models I</script> the uniqueness constraint cannot
-  fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-808-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-808">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-809-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-809">W \models I'</script>.</p>
+  or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-804-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-804">I</script> is in normal form then we are
+  done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-805-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-805">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_MathML" id="MathJax-Element-806-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-806">W \models I</script> the uniqueness constraint cannot
+  fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-807-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-807">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-808-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-808">W \models I'</script>.</p>
 <p>
   For part 3, the arguments are as
   in the previous section for each constraint. </p>
   <p>Finally, for part 4,
-  suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-810-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-810">W \models I</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-811-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-811">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-812-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-812">I'</script> is the normal
-  form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-813-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-813">I</script> by part 2.  By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-814-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-814">I'</script> satisfies all of the
-  remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-815-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-815">I</script> is valid.</p>
+  suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-809-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-809">W \models I</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-810-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-810">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-811-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-811">I'</script> is the normal
+  form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-812-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-812">I</script> by part 2.  By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-813-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-813">I'</script> satisfies all of the
+  remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-814-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-814">I</script> is valid.</p>
   </div>
 
   </section>
@@ -3651,15 +3650,15 @@
   structures, and show that a valid PROV instance has a model.</p>
 
   
-  <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-816-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-816">I</script> be a valid PROV instance that is in normal form.
-  We define a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-817-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-817">M(I)</script> as follows, by giving the sets,
+  <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-815-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-815">I</script> be a valid PROV instance that is in normal form.
+  We define a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-816-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-816">M(I)</script> as follows, by giving the sets,
   functions and relations specified in the components in <a href="#structures">Section 3</a>.</p>
 
   <section id="sets">
 <h4><span class="secno">6.2.1 </span>Sets</h4>
-  <p> The sets of structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-818-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-818">M(I)</script> are: </p>
-
-  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-819-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>p</mi><mi>l</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">≠</mo><mo stretchy="false">−</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>q</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>q</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-819">
+  <p> The sets of structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-817-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-817">M(I)</script> are: </p>
+
+  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-818-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>p</mi><mi>l</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">≠</mo><mo stretchy="false">−</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>q</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>q</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-818">
   \begin{eqnarray*}
   Entities &=& \{id \mid entity(id,attrs) \in I\}\\
   Plans &=& \{pl \mid wasAssociatedWith(id,ag,act,pl,attrs) \in I, pl
@@ -3694,28 +3693,28 @@
   Objects &=& Entities \cup Activities \cup Agents \cup Influences\\
   \end{eqnarray*}
   </script>
-<p>In the definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-820-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-820">Activities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-821-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-821">Generations</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-822-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-822">Usages</script> we
-  write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-823-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-823">a_{id}</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-824-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-824">g_{id}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-825-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-825">u_{id}</script> respectively to indicate
+<p>In the definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-819-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-819">Activities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-820-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-820">Generations</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-821-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-821">Usages</script> we
+  write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-822-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-822">a_{id}</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-823-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-823">g_{id}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-824-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-824">u_{id}</script> respectively to indicate
   additional activities, generations and usages added for imprecise derivations.
 </p>
-  <p> In addition, to define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-826-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-826">Things</script>, we introduce an
-  equivalence relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-827-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-827">Entities</script> as follows:
+  <p> In addition, to define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-825-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-825">Things</script>, we introduce an
+  equivalence relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-826-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-826">Entities</script> as follows:
   </p>
-  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-828-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">≡</mo><msub><mi>e</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-828">e_1 \equiv e_2 \iff alternateOf(e_1,e_2) \in I</script>
+  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-827-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">≡</mo><msub><mi>e</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-827">e_1 \equiv e_2 \iff alternateOf(e_1,e_2) \in I</script>
   <p>The fact that this is an equivalence relation follows from the
-  fact that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-829-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-829">I</script> is in normal form, since the constraints on
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-830-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-830">alternateOf</script> ensure that it is an equivalence relation.  Recall
-  that given an equivalence relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-831-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-831">\equiv</script> on some set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-832-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-832">X</script>, the
-  <em>equivalence class</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-833-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-833">x \in X</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-834-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">≡</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-834">[x]_\equiv = \{y
+  fact that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-828-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-828">I</script> is in normal form, since the constraints on
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-829-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-829">alternateOf</script> ensure that it is an equivalence relation.  Recall
+  that given an equivalence relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-830-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-830">\equiv</script> on some set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-831-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-831">X</script>, the
+  <em>equivalence class</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-832-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-832">x \in X</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-833-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">≡</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-833">[x]_\equiv = \{y
   \in X \mid x
-  \equiv y\}</script>.  The <em>quotient</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-835-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-835">X</script> by an equivalence
-  relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-836-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-836">X</script> is the set of equivalence classes, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-837-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-837">X_\equiv =
+  \equiv y\}</script>.  The <em>quotient</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-834-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-834">X</script> by an equivalence
+  relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-835-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-835">X</script> is the set of equivalence classes, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-836-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-836">X_\equiv =
   \{[x]_\equiv \mid x \in X\}</script>.  Now we
-  define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-838-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-838">Things</script> as the quotient of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-839-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-839">\equiv</script>-equivalence classes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-840-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-840">Entities</script>.</p>
-
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-841-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msub><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">≡</mo></mrow></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-841">Things = Entities /_{\equiv} = \{[e]_\equiv \mid e \in Entities\}</script>
-
-<p> Observe that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-842-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-842">I</script> is normalized and valid, entities and
+  define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-837-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-837">Things</script> as the quotient of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-838-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-838">\equiv</script>-equivalence classes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-839-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-839">Entities</script>.</p>
+
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-840-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msub><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">≡</mo></mrow></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-840">Things = Entities /_{\equiv} = \{[e]_\equiv \mid e \in Entities\}</script>
+
+<p> Observe that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-841-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-841">I</script> is normalized and valid, entities and
 activities are disjoint, the influences are disjoint from entities,
 activities, and agents, 
 and the different subsets of events and influences are pairwise
@@ -3724,10 +3723,10 @@
 <section id="functions">
 <h4><span class="secno">6.2.2 </span>Functions</h4>
 
-<p> First, we consider the functions associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-843-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-843">Entities</script>.  We
-employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-844-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-844">events:Entities \to P(Events)</script> that collects the set of all
-events in which <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-845-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-845">e</script> participated.</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-846-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>v</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">=</mo><mi>v</mi><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-846">
+<p> First, we consider the functions associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-842-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-842">Entities</script>.  We
+employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-843-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-843">events:Entities \to P(Events)</script> that collects the set of all
+events in which <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-844-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-844">e</script> participated.</p>
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-845-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>v</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">=</mo><mi>v</mi><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-845">
 \begin{eqnarray*}
 events(e) &=& \{id \mid used(id,a,e,t,attrs) \in I\}\\
 &\cup& \{id \mid wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
@@ -3739,10 +3738,10 @@
 thingOf(e) &=& [e]_\equiv
 \end{eqnarray*}
 </script>
-<p> Similarly, for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-847-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-847">Things</script>, we
-employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-848-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-848">events:Things \to P(Events)</script> that collects the set of all
+<p> Similarly, for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-846-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-846">Things</script>, we
+employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-847-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-847">events:Things \to P(Events)</script> that collects the set of all
 events in which one of the entities constituting the thing participated.</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-849-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-849">
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-848-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-848">
 \begin{eqnarray*}
 events(T) &=& \bigcup_{e \in T} events(e)\\
 lifetime(e) &=& \{time(e) \mid evt \in events(T)\}\\
@@ -3755,10 +3754,10 @@
   some of the times are symbolic?</p>
   </div></div>
 
-<p> The functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-850-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-850">startTime</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-851-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-851">endTime</script> mapping activities to
+<p> The functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-849-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-849">startTime</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-850-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-850">endTime</script> mapping activities to
   their start and end times is defined as follows:
   </p>
-  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-852-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><span style="display: inline-block; vertical-align: middle; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid; ">\begin{eqnarray*}<br>&nbsp;&nbsp;startTime(id)&nbsp;&amp;=&amp;&nbsp;t_1&nbsp;\text{&nbsp;where&nbsp;}&nbsp;activity(a,t_1,t_2,attrs)&nbsp;\in<br>&nbsp;&nbsp;I\\<br>&nbsp;&nbsp;&amp;&nbsp;\text{&nbsp;or&nbsp;}&nbsp;wasStartedBy(start,a,e,a',t_1,attrs)&nbsp;\in&nbsp;I\\<br>&nbsp;&nbsp;endTime(id)&nbsp;&amp;=&amp;&nbsp;t_2&nbsp;\text{&nbsp;where&nbsp;}&nbsp;activity(a,t_1,t_2,attrs)&nbsp;\in<br>&nbsp;&nbsp;I\\<br>&nbsp;&nbsp;&amp;&nbsp;\text{&nbsp;or&nbsp;}&nbsp;wasEndedBy(end,a,e,a',t_2,attrs)&nbsp;\in&nbsp;I\\</span></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-852">\begin{eqnarray*}
+  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-851-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><span style="display: inline-block; vertical-align: middle; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid; ">\begin{eqnarray*}<br>&nbsp;&nbsp;startTime(id)&nbsp;&amp;=&amp;&nbsp;t_1&nbsp;\text{&nbsp;where&nbsp;}&nbsp;activity(a,t_1,t_2,attrs)&nbsp;\in<br>&nbsp;&nbsp;I\\<br>&nbsp;&nbsp;&amp;&nbsp;\text{&nbsp;or&nbsp;}&nbsp;wasStartedBy(start,a,e,a',t_1,attrs)&nbsp;\in&nbsp;I\\<br>&nbsp;&nbsp;endTime(id)&nbsp;&amp;=&amp;&nbsp;t_2&nbsp;\text{&nbsp;where&nbsp;}&nbsp;activity(a,t_1,t_2,attrs)&nbsp;\in<br>&nbsp;&nbsp;I\\<br>&nbsp;&nbsp;&amp;&nbsp;\text{&nbsp;or&nbsp;}&nbsp;wasEndedBy(end,a,e,a',t_2,attrs)&nbsp;\in&nbsp;I\\</span></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-851">\begin{eqnarray*}
   startTime(id) &=& t_1 \text{ where } activity(a,t_1,t_2,attrs) \in
   I\\
   & \text{ or } wasStartedBy(start,a,e,a',t_1,attrs) \in I\\
@@ -3767,12 +3766,12 @@
   & \text{ or } wasEndedBy(end,a,e,a',t_2,attrs) \in I\\
 </script>
   <p>Note that the above definition is deterministic because the start
-  and end times in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-853-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-853">activity</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-854-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-854">wasStartedBy/wasEndedBy</script> statements
+  and end times in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-852-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-852">activity</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-853-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-853">wasStartedBy/wasEndedBy</script> statements
   must be equal</p>.
-<p> The function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-855-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-855">time</script> mapping <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-856-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-856">Events</script> to their <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-857-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-857">Times</script> is defined
+<p> The function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-854-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-854">time</script> mapping <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-855-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-855">Events</script> to their <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-856-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-856">Times</script> is defined
   as follows:
   </p>
-  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-858-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-858">\begin{eqnarray*}
+  <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-857-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-857">\begin{eqnarray*}
   time(id) &=& t \text{ where } used(id,a,e,t,attrs) \in I\\
   time(id) &=&  t \text{ where } wasGeneratedBy(id,e,a,t,attrs) \in I\\
 time(id) &=& t\text{ where } wasInvalidatedBy(id,e,a,t,attrs) \in I\\
@@ -3785,7 +3784,7 @@
   <p>Finally, the functions giving the interpretations of the
   different identified influences are as follows:
   </p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-859-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-859">\begin{eqnarray*}
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-858-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext>&nbsp;where&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-858">\begin{eqnarray*}
   used(id) &=& (a,e) \text{ where } used(id,a,e,t,attrs) \in I\\
   generated(id) &=&  (e,a) \text{ where } wasGeneratedBy(id,e,a,t,attrs) \in I\\
   invalidated(id) &=& (e,a) \text{ where } wasInvalidatedBy(id,e,a,t,attrs) \in I\\
@@ -3802,10 +3801,10 @@
   derivationPath(id) &=& e_2\cdot g_{id} \cdot a_{id} \cdot u_{id} \cdot e_1 \text{ where } wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\\
   \end{eqnarray*}
   </script>
-  <p>Note that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-860-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-860">I</script> is normalized and valid, by the uniqueness
+  <p>Note that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-859-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-859">I</script> is normalized and valid, by the uniqueness
   constraints these functions are all well-defined.  In the case for
   imprecise derivations, we generate additional activities, generations
-  and usages linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-861-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-861">e_2</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-862-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-862">e_1</script>.
+  and usages linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-860-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-860">e_2</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-861-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-861">e_1</script>.
   </p>
   <div class="remark">
 
@@ -3817,24 +3816,24 @@
 </section>
 <section id="relations">
 <h4><span class="secno">6.2.3 </span>Relations</h4>
-<p>We introduced a relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-863-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-863">\equiv</script> corresponding to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-864-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-864">alternateOf</script>
-  above, in defining <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-865-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-865">Things</script>, but this relation is not a component of
+<p>We introduced a relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-862-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-862">\equiv</script> corresponding to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-863-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-863">alternateOf</script>
+  above, in defining <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-864-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-864">Things</script>, but this relation is not a component of
   the semantics.</p>
     <p>The event ordering relation is defined as follows:</p>
-    <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-866-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><msub><mi>G</mi><mi>I</mi></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-866">evt \preceq evt' \iff (evt,evt') \in G_I</script>
-    <p> Here, we are using a slight abuse of notation: we write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-867-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-867">G_I</script>
-  for the directed graph that is used during validation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-868-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-868">I</script> to
+    <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-865-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><msub><mi>G</mi><mi>I</mi></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-865">evt \preceq evt' \iff (evt,evt') \in G_I</script>
+    <p> Here, we are using a slight abuse of notation: we write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-866-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-866">G_I</script>
+  for the directed graph that is used during validation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-867-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-867">I</script> to
   test for cycles amond event ordering constraints.  See Sec. 7.1 of PROV-CONSTRAINTS [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>].</p>
 
-    <p> Finally, the collection membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-869-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-869">MemberOf</script> is
+    <p> Finally, the collection membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-868-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-868">MemberOf</script> is
     defined as follows:</p>
-    <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-870-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-870">(e,c) \in MemberOf \iff memberOf(e,c) \in I</script>
+    <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-869-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-869">(e,c) \in MemberOf \iff memberOf(e,c) \in I</script>
     
 </section>
     <section id="axioms-1">
     <h4><span class="secno">6.2.4 </span>Axioms</h4>
 
-    <p>To verify that the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-871-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-871">M(I)</script> yields a PROV
+    <p>To verify that the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-870-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-870">M(I)</script> yields a PROV
     structure, we must ensure that all of the axioms and
     side-conditions in the components are satisfied.  As noted above,
     the disjointness constraints are satisfied by construction. </p>
@@ -3845,62 +3844,62 @@
 <h4><span class="secno">6.2.5 </span>Main results</h4>
 
 <p> The main results of this section are that if a valid PROV instance
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-872-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-872">I</script> normalizes to
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-873-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-873">I'</script>, then  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-874-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-874">M(I') \models I</script>, and that furthermore <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-875-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-875">M(I')</script>
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-871-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-871">I</script> normalizes to
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-872-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-872">I'</script>, then  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-873-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-873">M(I') \models I</script>, and that furthermore <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-874-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-874">M(I')</script>
     satisfies all of the inferences and constraints.  Thus, a form of
     completeness holds: every valid PROV instance has a model.</p>
 
 <div class="theorem" id="rule_40" data-count="40" data-title="Theorem 40 (rule_40)"><div class="ruleTitle"><a class="internalDFN" href="#rule_40">Theorem 40 (rule_40)</a></div>
-  <p>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-876-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-876">J</script> is a valid PROV instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-877-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-877">I</script> is a normal form for
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-878-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-878">J</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-879-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-879">M(I) \models J</script></p>
+  <p>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-875-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-875">J</script> is a valid PROV instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-876-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-876">I</script> is a normal form for
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-877-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-877">J</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-878-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-878">M(I) \models J</script></p>
   </div>
   <div class="proof">
     <p>
-    First, we consider the case where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-880-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-880">J</script> itself is a valid,
-  normalized PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-881-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-881">I</script>, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-882-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-882">M(I)</script>
-  be the corresponding structure.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-883-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-883">M(I)</script> is a PROV structure,
+    First, we consider the case where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-879-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-879">J</script> itself is a valid,
+  normalized PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-880-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-880">I</script>, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-881-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-881">M(I)</script>
+  be the corresponding structure.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-882-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-882">M(I)</script> is a PROV structure,
   satisfying all of the axioms (and hence all of the inferences and
   constraints) stated above.
     </p>
 
-    <p>Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-884-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-884">M(I) \models I</script>, as can be verified on a
+    <p>Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-883-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-883">M(I) \models I</script>, as can be verified on a
     case-by-case basis for each type of formula by considering its
-    semantics and the definition of the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-885-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-885">M</script>.  </p>
-
-    <p> To conclude, we need to show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-886-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-886">J</script> is not in normal
-    form, and norma,izes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-887-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-887">I</script>, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-888-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-888">M(I) \models J</script>.  WE can prove
+    semantics and the definition of the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-884-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-884">M</script>.  </p>
+
+    <p> To conclude, we need to show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-885-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-885">J</script> is not in normal
+    form, and norma,izes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-886-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-886">I</script>, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-887-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-887">M(I) \models J</script>.  WE can prove
     this by induction on the length of the sequence of normalization
-    steps.  The base case, when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-889-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-889">J = I</script>, is established already.
-    Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-890-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-890">J</script> normalizes in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-891-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></math></span></span></span><script type="math/tex" id="MathJax-Element-891">n+1</script> steps and we can perform one
-    normalization step on it to obtain <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-892-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-892">J'</script>, which normalizes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-893-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-893">I</script>
-    in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-894-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-894">n</script> steps.  By induction, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-895-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-895">M(I) \models J'</script>.  For
-    each possible normalization step, we must show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-896-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-896">M(I)
-    \models J'</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-897-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-897">M(I) \models J</script>.
+    steps.  The base case, when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-888-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-888">J = I</script>, is established already.
+    Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-889-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-889">J</script> normalizes in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-890-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></math></span></span></span><script type="math/tex" id="MathJax-Element-890">n+1</script> steps and we can perform one
+    normalization step on it to obtain <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-891-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-891">J'</script>, which normalizes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-892-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-892">I</script>
+    in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-893-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-893">n</script> steps.  By induction, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-894-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-894">M(I) \models J'</script>.  For
+    each possible normalization step, we must show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-895-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-895">M(I)
+    \models J'</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-896-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-896">M(I) \models J</script>.
     </p>
     <p>First consider inference steps.  These add information, that
-    is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-898-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">⊇</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-898">J' \supseteq J</script>.  Hence it is immediate that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-899-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-899">M(I) \models J</script>
-    since every formula in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-900-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-900">J</script> is in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-901-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-901">J'</script>, and all formulas of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-902-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-902">J'</script>
-    are satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-903-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-903">M(I)</script>.
+    is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-897-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">⊇</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-897">J' \supseteq J</script>.  Hence it is immediate that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-898-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-898">M(I) \models J</script>
+    since every formula in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-899-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-899">J</script> is in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-900-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-900">J'</script>, and all formulas of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-901-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-901">J'</script>
+    are satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-902-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-902">M(I)</script>.
     </p>
     <p>Next consider uniqueness constraint steps, which may involve
-    merging formulas.  That is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-904-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-904">J = J_0 \cup
+    merging formulas.  That is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-903-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-903">J = J_0 \cup
     \{r(id,a_1,\ldots,a_n,attrs_1), r(id,b_1,\ldots,b_n,attrs_2)\}</script>
-    and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-905-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-905">J' = S(J_0) \cup \{r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
-    attrs_2)\}</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-906-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-906">S</script> is a unifying substitution making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-907-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-907">S(a_i) =
-    S(b_i)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-908-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-908">i \in \{1,\ldots,n\}</script>.  Since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-909-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-909">M(I) \models J'</script>,
-    we must have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-910-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-910">M(I),\rho \models J'</script>  for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-911-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-911">\rho</script>, and therefore
-    we must also have that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-912-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-912">M(I),\rho \models S(J_0)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-913-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-913">M(I)\rho \models r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
-    attrs_2)</script>.  We can extend <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-914-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-914">\rho</script> to a valuation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-915-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-915">\rho'</script> such that
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-916-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-916">M(I),\rho' \models S(x_1) = x_i \wedge \cdots \wedge S(x_k) =
-    x_k</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-917-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-917">dom(S) = \{x_1,\ldots,x_k\}</script>.
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-918-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-918">M(I),\rho' \models J_0</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-919-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-919">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1\cup
-    attrs_2)</script>.  Moreover, since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-920-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-920">S</script> is a unifier, we also have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-921-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-921">M(I),\rho' \models r(id,b_1,\ldots,b_n,attrs_1\cup
+    and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-904-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-904">J' = S(J_0) \cup \{r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
+    attrs_2)\}</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-905-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-905">S</script> is a unifying substitution making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-906-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-906">S(a_i) =
+    S(b_i)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-907-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-907">i \in \{1,\ldots,n\}</script>.  Since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-908-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-908">M(I) \models J'</script>,
+    we must have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-909-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-909">M(I),\rho \models J'</script>  for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-910-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-910">\rho</script>, and therefore
+    we must also have that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-911-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-911">M(I),\rho \models S(J_0)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-912-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-912">M(I)\rho \models r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
+    attrs_2)</script>.  We can extend <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-913-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-913">\rho</script> to a valuation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-914-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-914">\rho'</script> such that
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-915-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-915">M(I),\rho' \models S(x_1) = x_i \wedge \cdots \wedge S(x_k) =
+    x_k</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-916-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-916">dom(S) = \{x_1,\ldots,x_k\}</script>.
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-917-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-917">M(I),\rho' \models J_0</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-918-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-918">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1\cup
+    attrs_2)</script>.  Moreover, since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-919-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-919">S</script> is a unifier, we also have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-920-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-920">M(I),\rho' \models r(id,b_1,\ldots,b_n,attrs_1\cup
     attrs_2)</script>.  Finally, since we can always remove attributes from an
     atomic formula without danaging its satisfiability, we can
-    conclude that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-922-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-922">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1)
+    conclude that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-921-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-921">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1)
     \wedge r(id,b_1,\ldots,b_n,    attrs_2)</script>.  To conclude, we have
-    shown <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-923-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-923">M(I) \models J_0 \cup \{ r(id,a_1,\ldots,a_n,attrs_1)
-   r(id,b_1,\ldots,b_n,    attrs_2)\}</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-924-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-924">M(I) \models J</script>, as
+    shown <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-922-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-922">M(I) \models J_0 \cup \{ r(id,a_1,\ldots,a_n,attrs_1)
+   r(id,b_1,\ldots,b_n,    attrs_2)\}</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-923-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-923">M(I) \models J</script>, as
     desired.
 </p>
 </div></section>
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