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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">R3</font> be   <a href="pnproc_1.html#NM6">process</a> of <font color="Maroon">N</font>;<br/>









<b>thus </b><a NAME="E1:99"/>
<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#K13" target="_self">concur</a> <font color="Maroon">R3</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">R1</font> <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#K13" target="_self">concur</a> <font color="Maroon">R3</font></span>)</span>
  <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="99_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="E1:99_1"/>
<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#K13" target="_self">concur</a> <font color="Maroon">R3</font>
 ;<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><b> such that </b><br/><a NAME="E3:99_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</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">C1</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> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R2</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">R3</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="E5:99_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">C1</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> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R2</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">R3</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><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="E7:99_1"/><i><font color="Green">E35</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</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">C2</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">R1</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">R2</font> ) )
 <b>by </b><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="E9:99_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">C2</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">R1</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">R2</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">n1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E11:99_1"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E12:99_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">q3</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> &amp; <font color="Maroon">q4</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E13:99_1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <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>, </i>;<br/>
<a NAME="E14:99_1"/>
 <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T99">FINSEQ_3:99</a></i>;<br/>
<a NAME="E15:99_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T125">FUNCT_1:125</a></i>;<br/>
<a NAME="E16:99_1"/><i><font color="Green">E123</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>;<br/>
<a NAME="E17:99_1"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E125</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q3</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q4</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
;<br/>
<i><font color="Green">E126</font></i>: <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T107">RELAT_1:107</a></i>
<br/>.= 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T153">RELAT_1:153</a></i>
<br/>.= 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>
<br/>.= 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
<br/>.= 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>
<br/>.= 
<font color="Maroon">q1</font>
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
;<br/>
<a NAME="E20:99_1"/><i><font color="Green">E130</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T87">RELAT_1:87</a></i>;<br/>
<a NAME="E21:99_1"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T99">RELAT_1:99</a></i>;<br/>
<a NAME="E22:99_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>;<br/>
<a NAME="E23:99_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E24:99_1"/><b>then </b><i><font color="Green">E131</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E25:99_1"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E26:99_1"/>
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E27:99_1"/><b>then </b><i><font color="Green">E133</font></i>: 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E28:99_1"/>
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E29:99_1"/><b>then </b><i><font color="Green">E134</font></i>: 
<font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E30:99_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E31:99_1"/><b>then </b><i><font color="Green">E135</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E32:99_1"/><i><font color="Green">E137</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E33:99_1"/><i><font color="Green">E138</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a>, </i>;<br/>
<a NAME="E34:99_1"/><i><font color="Green">E139</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E35:99_1"/><b>then </b><i><font color="Green">E140</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E36:99_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E37:99_1"/><b>then </b><i><font color="Green">E141</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E38:99_1"/><i><font color="Green">E142</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E39:99_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E40:99_1"/><b>then </b><i><font color="Green">E143</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q5</font> = <font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span>, <font color="Maroon">q6</font> = <font color="Maroon">q1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs</font> = <font color="Maroon">C1</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs1</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</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="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs2</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs3</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="pnproc_1.html#T20" target="_self">Th20</a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fss</font> = <font color="Maroon">q1</font>, <font color="Maroon">fss1</font> = <font color="Maroon">q5</font>, <font color="Maroon">fss2</font> = <font color="Maroon">q6</font> as    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">fs</font> <b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="txt" href="pnproc_1.html#E22"><i><font color="Green">Lemma80</font></i></a>, <a class="ref" href="pnproc_1.html#T13" target="_self">Th13</a>, <a class="ref" href="graph_2.html#D5">GRAPH_2:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fss3</font> = <font color="Maroon">q3</font>, <font color="Maroon">fss4</font> = <font color="Maroon">q4</font> as    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">fs1</font> <b>by </b><i>, <a class="ref" href="graph_2.html#D5">GRAPH_2:def 5</a></i>;<br/>
<a NAME="E48:99_1"/>
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs2</font> &amp; <font color="Maroon">fss1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fss</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss3</font></span>)</span></span>)</span></span>)</span> )
 
;<br/>
<a NAME="E49:99_1"/><b>then </b><i><font color="Green">E144</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q5</font>
 
<b>by </b><i><a class="ref" href="graph_2.html#T30">GRAPH_2:30</a></i>;<br/>
<a NAME="E50:99_1"/>
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs3</font> &amp; <font color="Maroon">fss2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fss</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss4</font></span>)</span></span>)</span></span>)</span> )
 
;<br/>
<a NAME="E51:99_1"/><b>then </b><i><font color="Green">E145</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q6</font>
 
<b>by </b><i><a class="ref" href="graph_2.html#T30">GRAPH_2:30</a></i>;<br/>
<a NAME="E52:99_1"/>
<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="E53:99_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">q5</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"><font color="Maroon">q6</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</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_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E54:99_1"/><b>then </b><i><font color="Green">E201</font></i>: 
( <font color="Maroon">q5</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>  &amp; <font color="Maroon">q6</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_1.html#T15">XBOOLE_1:15</a></i>;<br/>
<a NAME="E55:99_1"/><b>then </b><i><font color="Green">E202</font></i>: 
<font color="Maroon">q6</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E56:99_1"/><i><font color="Green">E203</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> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E57:99_1"/>
<font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E58:99_1"/><b>then </b>
<font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T28" target="_self">Th28</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E59:99_1"/><b>then </b><i><font color="Green">E204</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T27" target="_self">Th27</a>, <a class="ref" href="pnproc_1.html#T28" target="_self">Th28</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">q7</font> = <font color="Maroon">q6</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q2</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 href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></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"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
;<br/>
<a NAME="E62:99_1"/><b>then </b><i><font color="Green">E206</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E63:99_1"/><i><font color="Green">E207</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</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">C1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">q7</font> = <font color="Maroon">q7</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E65:99_1"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q5</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q7</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E66:99_1"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q7</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E67:99_1"/>
<font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</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="E68:99_1"/><b>then </b><i><font color="Green">E210</font></i>: 
<font color="Maroon">q5</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q7</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T26" target="_self">Th26</a>, , <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E69:99_1"/><i><font color="Green">E211</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q7</font>
 
<b>by </b><i/>;<br/>
<a NAME="E70:99_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q7</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q5</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D7" target="_self">Def7</a>, <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E71:99_1"/><b>then </b><i><font color="Green">E212</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E72:99_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E73:99_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self">Def8</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E74:99_1"/><b>then </b>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C3</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font> as   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font> <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E76:99_1"/><i><font color="Green">E213</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <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> <span class="p2">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E77:99_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q6</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E78:99_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q6</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">q8</font> = <font color="Maroon">q6</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span>, <font color="Maroon">q9</font> = <font color="Maroon">q2</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#D9" target="_self">Def9</a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E80:99_1"/>
 ex <font color="Olive">ss1</font>, <font color="Olive">ss2</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">ss1</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">ss2</font> &amp; <font color="Olive">ss1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">ss2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R3</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_4"><b>proof </b></a><div class="add">

<i><font color="Green">E218</font></i>: <font color="Maroon">C3</font> = 
<font color="Maroon">q7</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q8</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q9</font>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
;<br/>
<a NAME="E2:99_1_4"/><i><font color="Green">E219</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<a NAME="E3:99_1_4"/><i><font color="Green">E220</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<a NAME="E4:99_1_4"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T29" target="_self">Th29</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:99_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T171">RELAT_1:171</a></i>;<br/>
<a NAME="E6:99_1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_1.html#T137">FUNCT_1:137</a></i>;<br/>
<a NAME="E7:99_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E8:99_1_4"/><b>then </b><i><font color="Green">E221</font></i>: 
<font color="Maroon">q8</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q9</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#T34" target="_self">Th34</a>, </i>;<br/>
<a NAME="E9:99_1_4"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E10:99_1_4"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>;<br/>
<a NAME="E11:99_1_4"/><b>then </b><i><font color="Green">E222</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>;<br/>
<a NAME="E12:99_1_4"/><i><font color="Green">E223</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<b>then </b><i><font color="Green">E224</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span> <a href="relat_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T120">RELAT_1:120</a></i>
;<br/>
<a NAME="E14:99_1_4"/><i><font color="Green">E225</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E15:99_1_4"/><b>then </b><i><font color="Green">E226</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="pnproc_1.html#T32" target="_self">Th32</a>, <a class="ref" href="graph_2.html#T3">GRAPH_2:3</a></i>;<br/>
<i><font color="Green">E227</font></i>:  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q8</font> = 
<span class="p1">(<span class="default"><font color="Maroon">q6</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q6</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q6</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
;<br/>
<i><font color="Green">E228</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> <a href="relat_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T120">RELAT_1:120</a></i>
;<br/>
<a NAME="E18:99_1_4"/><i><font color="Green">E229</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="pnproc_1.html#T32" target="_self">Th32</a>, , <a class="ref" href="graph_2.html#T3">GRAPH_2:3</a></i>;<br/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q9</font> = 
<span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
;<br/>
<b>hence </b><a NAME="E20:99_1_4"/>
 ex <font color="Olive">ss1</font>, <font color="Olive">ss2</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">ss1</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">ss2</font> &amp; <font color="Olive">ss1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">ss2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R3</font> )
 <b>by </b><i>, , <a class="ref" href="pnproc_1.html#T23" target="_self">Th23</a>, , <a class="ref" href="pnproc_1.html#D10" target="_self">Def10</a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E81:99_1"/><b>then </b>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R3</font>
 
;<br/>
<b>hence </b><a NAME="E82:99_1"/>
<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> <span class="p1">(<span class="default"><font color="Maroon">R2</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R3</font></span>)</span>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a>, , <a class="ref" href="pnproc_1.html#T21" target="_self">Th21</a>, <a class="ref" href="pnproc_1.html#D7" target="_self">Def7</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="E2:99"/>
<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> <span class="p1">(<span class="default"><font color="Maroon">R2</font> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R3</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><b> such that </b><br/><a NAME="E4:99"/><i><font color="Green">E230</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</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">C1</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> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R3</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="E6:99"/><i><font color="Green">E231</font></i>: 
( <font color="Maroon">C1</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> <a href="pnproc_1.html#K13" target="_self">concur</a> <font color="Maroon">R3</font> )
 <b>by </b><i><a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><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="E8:99"/><i><font color="Green">E232</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</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">C2</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">R2</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">R3</font> ) )
 <b>by </b><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="E10:99"/><i><font color="Green">E233</font></i>: 
( <font color="Maroon">C2</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">R2</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">R3</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">n1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E12:99"/><i><font color="Green">E234</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E13:99"/><i><font color="Green">E235</font></i>: 
( <font color="Maroon">q3</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> &amp; <font color="Maroon">q4</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E14:99"/><b>then </b><i><font color="Green">E236</font></i>: 
 <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>, </i>;<br/>
<a NAME="E15:99"/>
 <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T99">FINSEQ_3:99</a></i>;<br/>
<a NAME="E16:99"/><b>then </b><i><font color="Green">E237</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T125">FUNCT_1:125</a></i>;<br/>
<a NAME="E17:99"/><i><font color="Green">E238</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>;<br/>
<a NAME="E18:99"/><b>then </b><i><font color="Green">E239</font></i>: 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E240</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
;<br/>
<i><font color="Green">E241</font></i>: <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T107">RELAT_1:107</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T153">RELAT_1:153</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>
<br/>.= 
<font color="Maroon">q2</font>
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>
;<br/>
<a NAME="E21:99"/><i><font color="Green">E242</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T87">RELAT_1:87</a></i>;<br/>
<a NAME="E22:99"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T99">RELAT_1:99</a></i>;<br/>
<a NAME="E23:99"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>;<br/>
<a NAME="E24:99"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E25:99"/><b>then </b><i><font color="Green">E243</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n1</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E26:99"/><i><font color="Green">E244</font></i>: 
<font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E27:99"/>
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E28:99"/><b>then </b><i><font color="Green">E245</font></i>: 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E29:99"/>
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E30:99"/><b>then </b><i><font color="Green">E246</font></i>: 
<font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E31:99"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E32:99"/><b>then </b><i><font color="Green">E247</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E33:99"/><i><font color="Green">E248</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E34:99"/><i><font color="Green">E249</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T14" target="_self">Th14</a>, </i>;<br/>
<a NAME="E35:99"/><i><font color="Green">E250</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E36:99"/><b>then </b><i><font color="Green">E251</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E37:99"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q3</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E38:99"/><b>then </b><i><font color="Green">E252</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#D6" target="_self">Def6</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E39:99"/><i><font color="Green">E253</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E40:99"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q4</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E41:99"/><b>then </b><i><font color="Green">E254</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q5</font> = <font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q3</font></span>)</span></span>)</span></span>)</span>, <font color="Maroon">q6</font> = <font color="Maroon">q2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q4</font></span>)</span></span>)</span></span>)</span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs</font> = <font color="Maroon">C1</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs1</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q2</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</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="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs2</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q3</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="pnproc_1.html#T16" target="_self">Th16</a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fs3</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <b>by </b><i><a class="ref" href="pnproc_1.html#T20" target="_self">Th20</a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fss</font> = <font color="Maroon">q2</font>, <font color="Maroon">fss1</font> = <font color="Maroon">q5</font>, <font color="Maroon">fss2</font> = <font color="Maroon">q6</font> as    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">fs</font> <b>by </b><i><a class="ref" href="pnproc_1.html#D4" target="_self">Def4</a>, <a class="txt" href="pnproc_1.html#E22"><i><font color="Green">Lemma80</font></i></a>, <a class="ref" href="pnproc_1.html#T13" target="_self">Th13</a>, <a class="ref" href="graph_2.html#D5">GRAPH_2:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fss3</font> = <font color="Maroon">q3</font>, <font color="Maroon">fss4</font> = <font color="Maroon">q4</font> as    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">fs1</font> <b>by </b><i>, <a class="ref" href="graph_2.html#D5">GRAPH_2:def 5</a></i>;<br/>
<a NAME="E49:99"/>
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs2</font> &amp; <font color="Maroon">fss1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fss</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss3</font></span>)</span></span>)</span></span>)</span> )
 
;<br/>
<a NAME="E50:99"/><b>then </b><i><font color="Green">E255</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q5</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font>
 
<b>by </b><i>, <a class="ref" href="graph_2.html#T30">GRAPH_2:30</a></i>;<br/>
<a NAME="E51:99"/>
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs1</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fs3</font> &amp; <font color="Maroon">fss2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fss</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">fss4</font></span>)</span></span>)</span></span>)</span> )
 
;<br/>
<a NAME="E52:99"/><b>then </b><i><font color="Green">E256</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q4</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q6</font>
 
<b>by </b><i><a class="ref" href="graph_2.html#T30">GRAPH_2:30</a></i>;<br/>
<a NAME="E53:99"/>
<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="E54:99"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q5</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</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_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E55:99"/><b>then </b><i><font color="Green">E257</font></i>: 
( <font color="Maroon">q1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q5</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> <font color="Maroon">q6</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T15">XBOOLE_1:15</a></i>;<br/>
<a NAME="E56:99"/><b>then </b><i><font color="Green">E258</font></i>: 
<font color="Maroon">q1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q5</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E57:99"/><i><font color="Green">E259</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> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E58:99"/>
<font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E59:99"/><b>then </b>
<font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T28" target="_self">Th28</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E60:99"/><b>then </b><i><font color="Green">E260</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T27" target="_self">Th27</a>, <a class="ref" href="pnproc_1.html#T28" target="_self">Th28</a>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">q7</font> = <font color="Maroon">q1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q5</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 href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</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"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q6</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>
;<br/>
<a NAME="E63:99"/><b>then </b><i><font color="Green">E261</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E64:99"/><i><font color="Green">E262</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C1</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">C1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">q7</font> = <font color="Maroon">q7</font> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E66:99"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q7</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q6</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E67:99"/><i><font color="Green">E264</font></i>: 
<font color="Maroon">q7</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</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">q6</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E68:99"/>
<font color="Maroon">q5</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">q6</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="E69:99"/><b>then </b><i><font color="Green">E265</font></i>: 
<font color="Maroon">q7</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q6</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T26" target="_self">Th26</a>, , <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E70:99"/><i><font color="Green">E266</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q7</font>
 
<b>by </b><i/>;<br/>
<a NAME="E71:99"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q7</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">q6</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D7" target="_self">Def7</a>, <a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E72:99"/><b>then </b><i><font color="Green">E267</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E73:99"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E74:99"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#D8" target="_self">Def8</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E75:99"/><b>then </b>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C3</font> =  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font> as   <a href="pnproc_1.html#NM5">firing-sequence</a> of <font color="Maroon">N</font> <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E77:99"/><i><font color="Green">E268</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> <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> <span class="p2">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E78:99"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E79:99"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">q8</font> = <font color="Maroon">q1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span>, <font color="Maroon">q9</font> = <font color="Maroon">q5</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> as   <a href="finseq_1.html#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="pnproc_1.html#D9" target="_self">Def9</a>, <a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E81:99"/>
 ex <font color="Olive">ss1</font>, <font color="Olive">ss2</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">ss1</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">ss2</font> &amp; <font color="Olive">ss1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">ss2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss1</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">ss2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_5"><b>proof </b></a><div class="add">

<i><font color="Green">E269</font></i>: <font color="Maroon">C3</font> = 
<font color="Maroon">q7</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q8</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">q9</font>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
;<br/>
<a NAME="E2:99_5"/><i><font color="Green">E270</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<a NAME="E3:99_5"/><i><font color="Green">E271</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<a NAME="E4:99_5"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T29" target="_self">Th29</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:99_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T171">RELAT_1:171</a></i>;<br/>
<a NAME="E6:99_5"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_1.html#T137">FUNCT_1:137</a></i>;<br/>
<a NAME="E7:99_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E8:99_5"/><b>then </b><i><font color="Green">E272</font></i>: 
<font color="Maroon">q8</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">q9</font>
 
<b>by </b><i>, <a class="ref" href="pnproc_1.html#T34" target="_self">Th34</a>, </i>;<br/>
<a NAME="E9:99_5"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E10:99_5"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>;<br/>
<a NAME="E11:99_5"/><b>then </b><i><font color="Green">E273</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>;<br/>
<a NAME="E12:99_5"/><i><font color="Green">E274</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T182">RELAT_1:182</a></i>;<br/>
<b>then </b><i><font color="Green">E275</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font></span>)</span> <a href="relat_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q1</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T120">RELAT_1:120</a></i>
;<br/>
<a NAME="E14:99_5"/><i><font color="Green">E276</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<a NAME="E15:99_5"/><b>then </b><i><font color="Green">E277</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="pnproc_1.html#T32" target="_self">Th32</a>, <a class="ref" href="graph_2.html#T3">GRAPH_2:3</a></i>;<br/>
<i><font color="Green">E278</font></i>:  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q8</font> = 
<span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q8</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q1</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
;<br/>
<i><font color="Green">E279</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font></span>)</span> <a href="relat_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q5</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T120">RELAT_1:120</a></i>
;<br/>
<a NAME="E18:99_5"/><i><font color="Green">E280</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T31" target="_self">Th31</a>, <a class="ref" href="pnproc_1.html#T32" target="_self">Th32</a>, , <a class="ref" href="graph_2.html#T3">GRAPH_2:3</a></i>;<br/>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q9</font> = 
<span class="p1">(<span class="default"><font color="Maroon">q5</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon">q5</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q7</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q9</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q5</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>
;<br/>
<b>hence </b><a NAME="E20:99_5"/>
 ex <font color="Olive">ss1</font>, <font color="Olive">ss2</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">ss1</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">ss2</font> &amp; <font color="Olive">ss1</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">ss2</font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Olive">ss1</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">ss2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R2</font> )
 <b>by </b><i>, <a class="ref" href="pnproc_1.html#T21" target="_self">Th21</a>, , <a class="ref" href="pnproc_1.html#D10" target="_self">Def10</a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E82:99"/><b>then </b>
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">q7</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/>
<b>hence </b><a NAME="E83:99"/>
<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#K13" target="_self">concur</a> <font color="Maroon">R3</font>
 <b>by </b><i><a class="ref" href="pnproc_1.html#D1" target="_self">Def1</a>, , <a class="ref" href="pnproc_1.html#T23" target="_self">Th23</a>, <a class="ref" href="pnproc_1.html#D7" target="_self">Def7</a>, </i>;<br/>


</div>
