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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>









<b>assume </b><a NAME="E1:70"/><i><font color="Green">E57</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="graph_5.html#R6" target="_self">is_weight_of</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E2:70"/><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="graph_5.html#K9" target="_self">RealSequence</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="graph_5.html#E1:70"><i><font color="Green">E57</font></i></a>, <a class="ref" href="graph_5.html#D15" target="_self">Def15</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:70"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="graph_5.html#E1:70"><i><font color="Green">E57</font></i></a>, <a class="ref" href="graph_5.html#T2" target="_self">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="graph_5.html#E4:70"><i><font color="Green">E59</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>9</sub></font>
;<br/>

<b>thus </b><a NAME="E6:70"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="graph_5.html#E4:70"><i><font color="Green">E59</font></i></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="graph_5.html#E1:70"><i><font color="Green">E57</font></i></a>, <a class="txt" href="graph_5.html#E2:70"><i><font color="Green">E58</font></i></a>, <a class="txt" href="graph_5.html#E4:70"><i><font color="Green">E59</font></i></a>, <a class="ref" href="graph_5.html#D15" target="_self">Def15</a></i>;<br/>


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