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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">V</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">pe</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">qe</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font>;<br/>









<b>assume </b><a NAME="E1:32"/><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><a href="graph_5.html#K2" target="_self">vertices</a> <span class="p2">(<span class="default"><font color="Maroon">pe</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">qe</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 ;<br/>

<a NAME="E2:32"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">pe</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">pe</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">qe</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T42">FINSEQ_1:42</a></i>;<br/>
<a NAME="E3:32"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">qe</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">pe</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">qe</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T43">FINSEQ_1:43</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
( <span class="p1">(<span class="default"><a href="graph_5.html#K2" target="_self">vertices</a> <font color="Maroon">pe</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <span class="p1">(<span class="default"><a href="graph_5.html#K2" target="_self">vertices</a> <font color="Maroon">qe</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 <b>by </b><i>, , </i>;<br/>


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