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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">R1</font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">R2</font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">N</font>;<br/><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="E1:100"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">R2</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>consider </b><font color="Maroon">C1</font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font>, <font color="Maroon">C2</font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E4:100"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">C1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> &amp; <font color="Maroon">C2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>set </b><font color="Maroon">q1</font> = <font color="Maroon">C1</font>;<br/>
<b>set </b><font color="Maroon">q2</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C1</font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">C2</font>;<br/>
<b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">C1</font> as   <a href="finseq_1.html#NM1">FinSequence</a> ;<br/>
<a NAME="E6:100"/>
(  <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;  <a href="finseq_1.html#K15">Seq</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C1</font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">C2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font> )
 
<b>by </b><i>, <a class="ref" href="graph_2.html#T24">GRAPH_2:24</a></i>;<br/>
<a NAME="E7:100"/><b>then </b>
( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C1</font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">C2</font></span>)</span> &amp; <font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C1</font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">C2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C1</font></span>)</span> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">C2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> )
 
<b>by </b><i>, , <a class="ref" href="pnproc_1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E8:100"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font> :  ex <font color="Olive">q1</font>, <font color="Olive">q2</font> being  <a href="finseq_1.html#NM4">FinSubsequence</a> st <br/>( <font color="Olive">a</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> <font color="Maroon">R1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> ) </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E9:100"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R1</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R2</font>
 ;<br/>


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