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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">W</font> be   <a href="funct_1.html#NM1">Function</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">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>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>assume </b><a NAME="E1:70"/><i><font color="Green">E39</font></i>: 
(  <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> <font color="Maroon">pe</font> &amp; <font color="Maroon">W</font> <a href="graph_5.html#R6" target="_self">is_weight_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">qe</font> )
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font>;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">qe</font>,<font color="Maroon">W</font>;<br/>
<a NAME="E2:70"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">qe</font>,<font color="Maroon">W</font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">qe</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="graph_5.html#T5" target="_self">Th5</a>, </i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:70"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">pe</font> &amp; <font color="Maroon">qe</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pe</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="graph_5.html#T5" target="_self">Th5</a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">j</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="graph_5.html#T6" target="_self">Th6</a></i>;<br/>
<b>take </b>
<font color="Maroon">j</font>
;<br/>

<b>thus </b><a NAME="E6:70"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">pe</font>
 <b>by </b><i><a class="ref" href="graph_5.html#T6" target="_self">Th6</a></i>;<br/>

<b>thus </b><a NAME="E7:70"/>
<span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">pe</font>,<font color="Maroon">W</font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">qe</font>,<font color="Maroon">W</font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="graph_5.html#T5" target="_self">Th5</a>, , <a class="ref" href="graph_5.html#T6" target="_self">Th6</a>, </i>;<br/>


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