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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">W</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c3">G</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>;<br/><b>let </b><font color="Maroon" title="c4">qe</font>, <font color="Maroon" title="c5">pe</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">G</font>;<br/>









<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E53">A1</font></i>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">qe</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">pe</font> &amp; <font color="Maroon" title="c2">W</font> <a href="graph_5.html#R6" title="GRAPH_5:pred.6">is_weight_of</a> <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">qe</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">f</font> =  <a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c5">pe</font>,<font color="Maroon" title="c2">W</font>;<br/>
<b>set </b><font color="Maroon" title="c7">g</font> =  <a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c4">qe</font>,<font color="Maroon" title="c2">W</font>;<br/>
<a NAME="E2:68"/><i><font color="Green" title="E54">A2</font></i>: 
<span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c4">qe</font>,<font color="Maroon" title="c2">W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">qe</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="graph_5.html#E1:68"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="graph_5.html#D15" target="_self" title="GRAPH_5:def.15">Def15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:68"/><i><font color="Green" title="E55">A3</font></i>: 
( <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">pe</font> &amp; <font color="Maroon" title="c4">qe</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">pe</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> )
 <b>by </b><i><a class="txt" href="graph_5.html#E1:68"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="graph_5.html#T2" target="_self" title="GRAPH_5:th.2">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">j</font> = <font color="Maroon" title="c8">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="graph_5.html#E4:68"><i><font color="Green" title="E55">A3</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">j</font>
;<br/>

<b>thus </b><a NAME="E6:68"/>
<font color="Maroon" title="c9">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">pe</font>
 <b>by </b><i><a class="txt" href="graph_5.html#E4:68"><i><font color="Green" title="E55">A3</font></i></a></i>;<br/>

<b>thus </b><a NAME="E7:68"/>
<span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c5">pe</font>,<font color="Maroon" title="c2">W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_5.html#K9" title="GRAPH_5:func.9">RealSequence</a> <font color="Maroon" title="c4">qe</font>,<font color="Maroon" title="c2">W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
 <b>by </b><i><a class="txt" href="graph_5.html#E1:68"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="graph_5.html#E2:68"><i><font color="Green" title="E54">A2</font></i></a>, <a class="txt" href="graph_5.html#E4:68"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="graph_5.html#D15" target="_self" title="GRAPH_5:def.15">Def15</a></i>;<br/>


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