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<b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">v1</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v2</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v3</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v4</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:44"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">e</font> <a href="graph_1.html#R2">joins</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font>
 <b>and </b><br/><a NAME="E2:44"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">e</font> <a href="graph_1.html#R2">joins</a> <font color="Maroon">v3</font>,<font color="Maroon">v4</font>
 ;<br/>

<a NAME="E3:44"/>
( ( ( the <a href="graph_1.html#U3">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> &amp; the <a href="graph_1.html#U4">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> ) or ( the <a href="graph_1.html#U3">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> &amp; the <a href="graph_1.html#U4">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> ) ) &amp; ( ( the <a href="graph_1.html#U3">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v3</font> &amp; the <a href="graph_1.html#U4">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v4</font> ) or ( the <a href="graph_1.html#U3">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v4</font> &amp; the <a href="graph_1.html#U4">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v3</font> ) ) )
 
<b>by </b><i><a class="ref" href="graph_2.html#T3" target="_self">Th3</a>, , <a class="ref" href="graph_1.html#D9">GRAPH_1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E4:44"/>
( ( <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v3</font> &amp; <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v4</font> ) or ( <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v4</font> &amp; <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v3</font> ) )
 ;<br/>


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