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<b>let </b><font color="Maroon">P</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">N</font> be    <a href="pnproc_1.html#M3" target="_self">Petri_net</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">N</font>;<br/>





<b>thus </b><a NAME="E1:126"/>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K15" target="_self">NeutralProcess</a> <font color="Maroon">N</font></span>)</span> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:126_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K15" target="_self">NeutralProcess</a> <font color="Maroon">N</font></span>)</span> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R</font>
 ;<br/>

<b>then consider </b><font color="Maroon">C</font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E3:126_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp;  ex <font color="Olive">q1</font>, <font color="Olive">q2</font> being  <a href="finseq_1.html#NM4">FinSubsequence</a> st <br/>( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Olive">q1</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">q2</font> &amp; <font color="Olive">q1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">q2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">q1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2">&lt;*&gt;</a> <font color="Maroon">N</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> ) )
 ;<br/>
<b>consider </b><font color="Maroon">q1</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a>, <font color="Maroon">q2</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E5:126_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q2</font> &amp; <font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2">&lt;*&gt;</a> <font color="Maroon">N</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E6:126_1"/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D5" target="_self">Def5</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:126_1"/><b>then </b>
<font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:126_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a>, <a class="ref" href="pnproc_1.html#D5" target="_self">Def5</a>, <a class="ref" href="graph_2.html#T24">GRAPH_2:24</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:126"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">C</font> = <font color="Maroon">x</font> as   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font> ;<br/>
<b>reconsider </b><font color="Maroon">q1</font> =  <a href="lang1.html#K2">&lt;*&gt;</a> <font color="Maroon">N</font>, <font color="Maroon">q2</font> = <font color="Maroon">C</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> ;<br/>
<a NAME="E5:126"/>
<font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<a NAME="E6:126"/><b>then </b>
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; <a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> &amp; <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="lang1.html#K2">&lt;*&gt;</a> <font color="Maroon">N</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q2</font> )
 
<b>by </b><i><a class="ref" href="graph_2.html#T24">GRAPH_2:24</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E7:126"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K15" target="_self">NeutralProcess</a> <font color="Maroon">N</font></span>)</span> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<br/>


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