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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">fs</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">fss</font> be    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">fs</font>;<br/>





<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:6"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E3:6"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">fss</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fss</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">fss</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>;<br/>
<a NAME="E4:6"/>
 <a href="relset_1.html#K5">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">fss</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fss</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D13">FINSEQ_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
 <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">fss</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_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">fss</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


</div>
