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<b>reconsider </b><font color="Maroon">V</font> = the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D8">GRAPH_1:def 8</a></i>;<br/>
<a NAME="E2:50_1_1"/>
the <a href="graph_1.html#U1">Vertices</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" target="_self">AddNewEdge</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="txt" href="graph_3.html#E2"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:50_1_1"/>
the <a href="graph_1.html#U1">Vertices</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" target="_self">AddNewEdge</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="graph_1.html#D8">GRAPH_1:def 8</a><br/>

<b>reconsider </b><font color="Maroon">E</font> = the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D8">GRAPH_1:def 8</a></i>;<br/>
<a NAME="E5:50_1_1"/>
the <a href="graph_1.html#U2">Edges</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" target="_self">AddNewEdge</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="graph_3.html#E2"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:50_1_1"/>
the <a href="graph_1.html#U2">Edges</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" target="_self">AddNewEdge</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 ;<br/>


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