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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">P1</font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">P2</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="E1:120"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R2</font></span>)</span> <a href="pnproc_1.html#K12" target="_self">before</a> <span class="p1">(<span class="default"><font color="Maroon">P1</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">P2</font></span>)</span>
 ;<br/>

<b>then 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="E3:120"/><i><font color="Green">E29</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> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R2</font> &amp; <font color="Maroon">C2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P1</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">P2</font> )
 ;<br/>
<b>consider </b><font color="Maroon">C3</font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E5:120"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C3</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">C3</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> ) )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<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="E7:120"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">C3</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> <font color="Maroon">R1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>consider </b><font color="Maroon">C4</font> being   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font><b> such that </b><br/><a NAME="E9:120"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C4</font> &amp;  ex <font color="Olive">q3</font>, <font color="Olive">q4</font> being  <a href="finseq_1.html#NM4">FinSubsequence</a> st <br/>( <font color="Maroon">C4</font> <a href="hidden.html#R1">=</a> <font color="Olive">q3</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">q4</font> &amp; <font color="Olive">q3</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">q4</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">q3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">q4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font> ) )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a></i>;<br/>
<b>consider </b><font color="Maroon">q3</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a>, <font color="Maroon">q4</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E11:120"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">C4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q3</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q4</font> &amp; <font color="Maroon">q3</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q4</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P2</font> )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> as   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font> ;<br/>
<b>reconsider </b><font color="Maroon">q5</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">q3</font>, <font color="Maroon">q6</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">q4</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> ;<br/>
<a NAME="E14:120"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">q3</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">q4</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D5" target="_self">Def5</a>, , , <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E15:120"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q5</font> &amp; <font color="Maroon">q2</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q6</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E16:120"/>
<font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/>
<a NAME="E17:120"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">ss</font> = <font color="Maroon">C2</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> ;<br/>
<a NAME="E19:120"/><i><font color="Green">E123</font></i>: 
( <font color="Maroon">q5</font> <a href="tarski.html#R1">c=</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">ss</font> &amp; <font color="Maroon">q6</font> <a href="tarski.html#R1">c=</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">ss</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, </i>;<br/>
<a NAME="E20:120"/>
<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> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E21:120"/><b>then </b>
( <font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> <a href="lang1.html#K1">^</a> <font color="Maroon">C2</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T21" target="_self">Th21</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E22:120"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T19" target="_self">Th19</a>, <a class="ref" href="pnproc_1.html#T20" target="_self">Th20</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">ss1</font> = <font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q5</font>, <font color="Maroon">ss2</font> = <font color="Maroon">q2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q6</font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="ref" href="grfunc_1.html#T31">GRFUNC_1:31</a></i>;<br/>
<a NAME="E24:120"/><i><font color="Green">E124</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E25:120"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">ss1</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">ss2</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">ss1</font> = <font color="Maroon">ss1</font>, <font color="Maroon">ss2</font> = <font color="Maroon">ss2</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#T23" target="_self">Th23</a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<i><font color="Green">E125</font></i>: <font color="Maroon">ss1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">ss2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4">(<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">q3</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q2</font></span>)</span> <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">q4</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<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">q3</font></span>)</span></span>)</span> <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">q4</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<font color="Maroon">C1</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<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">q4</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pnproc_1.html#D5" target="_self">Def5</a>, , <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<font color="Maroon">C1</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>
<b>by </b><i>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, </i>
<br/>.= 
<font color="Maroon">C</font>
<b>by </b><i/>
;<br/>
<a NAME="E28:120"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">ss1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">ss2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_2"><b>proof </b></a><div class="add">

<a NAME="E1:120_2"/>
( <font color="Maroon">ss1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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">q3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font></span>)</span> &amp; <font color="Maroon">ss1</font> <a href="xboole_0.html#K3">/\</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">q4</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<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">q4</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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">q3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<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">q4</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E2:120_2"/><b>then </b><i><font color="Green">E130</font></i>: 
<font color="Maroon">ss1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">ss2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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">q3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<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">q4</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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">q3</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<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">q4</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E3:120_2"/><i><font color="Green">E131</font></i>: 
<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> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E4:120_2"/>
( <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">q3</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q2</font> &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">q4</font> )
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, </i>;<br/>
<a NAME="E5:120_2"/><b>then </b><i><font color="Green">E132</font></i>: 
( <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">q3</font></span>)</span> <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>  &amp; <font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</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">q4</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:120_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, </i>;<br/>
<a NAME="E7:120_2"/><b>then </b>
 <a href="relat_1.html#K1">dom</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">q3</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</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">q4</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:120_2"/><b>then </b>
<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">q3</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">q4</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:120_2"/>
<font color="Maroon">ss1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">ss2</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#T28" target="_self">Th28</a>, <a class="ref" href="pnproc_1.html#T29" target="_self">Th29</a>, <a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">ss3</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E30:120"/><i><font color="Green">E133</font></i>: 
( <font color="Maroon">ss3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ss1</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">ss3</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="pnproc_1.html#T13" target="_self">Th13</a></i>;<br/>
<b>consider </b><font color="Maroon">ss4</font> being   <a href="finseq_1.html#NM4">FinSubsequence</a><b> such that </b><br/><a NAME="E32:120"/><i><font color="Green">E134</font></i>: 
( <font color="Maroon">ss4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ss2</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">ss4</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="pnproc_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E33:120"/><i><font color="Green">E135</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">ss1</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">P1</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="pnproc_1.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E34:120"/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">ss2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">P2</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="pnproc_1.html#T29" target="_self">Th29</a></i>;<br/>
<b>hence </b><a NAME="E35:120"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">R1</font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">P1</font></span>)</span> <a href="pnproc_1.html#K13" target="_self">concur</a> <span class="p1">(<span class="default"><font color="Maroon">R2</font> <a href="pnproc_1.html#K12" target="_self">before</a> <font color="Maroon">P2</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a>, <a class="ref" href="pnproc_1.html#T26" target="_self">Th26</a>, <a class="ref" href="pnproc_1.html#T27" target="_self">Th27</a>, <a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a></i>;<br/>


</div>
