<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">P</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">N</font> being   <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font><br/> for <font color="Olive" title="b2">e1</font>, <font color="Olive" title="b3">e2</font>, <font color="Olive" title="b4">e</font> being   <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Olive" title="b1">N</font> holds  <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b3">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b4">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">e1</font>,<font color="Olive" title="b4">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b3">e2</font>,<font color="Olive" title="b4">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">e</font>,<font color="Olive" title="b2">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">e</font>,<font color="Olive" title="b3">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span></span><br/><b>let </b><font color="Maroon" title="c2">N</font> be    <a href="pnproc_1.html#M4" title="PNPROC_1:mode.4">Petri_net</a> of <font color="Maroon" title="c1">P</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">e1</font>, <font color="Olive" title="b2">e2</font>, <font color="Olive" title="b3">e</font> being   <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Maroon" title="c2">N</font> holds  <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b1">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Olive" title="b3">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">e1</font>,<font color="Olive" title="b3">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">e2</font>,<font color="Olive" title="b3">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b3">e</font>,<font color="Olive" title="b1">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b3">e</font>,<font color="Olive" title="b2">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span></span><br/><b>let </b><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font>, <font color="Maroon" title="c5">e</font> be    <a href="pnproc_1.html#M5" title="PNPROC_1:mode.5">Element</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span></span><br/>









<a NAME="E1:81"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></i>;<br/>
<a NAME="E2:81"/><b>then </b><i><font color="Green" title="E50">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T48" target="_self" title="PNPROC_1:th.48">Th48</a></i>;<br/>
<a NAME="E3:81"/><i><font color="Green" title="E51">A2</font></i>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T49" target="_self" title="PNPROC_1:th.49">Th49</a></i>;<br/>
<a NAME="E4:81"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T49" target="_self" title="PNPROC_1:th.49">Th49</a></i>;<br/>
<b>hence </b><span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="pnproc_1.html#K11" title="PNPROC_1:func.11">concur</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> = 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
<b>by </b><i><a class="txt" href="#E2:81"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="#E3:81"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="enumset1.html#T45" title="ENUMSET1:th.45">ENUMSET1:45</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">e2</font>,<font color="Maroon" title="c5">e</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c3">e1</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>,<span class="p2"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c4">e2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T104" title="ENUMSET1:th.104">ENUMSET1:104</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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