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<b>reconsider </b><font color="Maroon" title="c4">V</font> = the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D8" title="GRAPH_1:def.8">GRAPH_1:def 8</a></i>;<br/>
<a NAME="E2:50_1_1"/>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" title="GRAPH_3:func.8">AddNewEdge</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="graph_3.html#D7" target="_self" title="GRAPH_3:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E3:50_1_1"/>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" title="GRAPH_3:func.8">AddNewEdge</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="graph_1.html#D8" title="GRAPH_1:def.8">GRAPH_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" title="GRAPH_3:func.8">AddNewEdge</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c5">E</font> = the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">G</font> as  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D8" title="GRAPH_1:def.8">GRAPH_1:def 8</a></i>;<br/>
<a NAME="E5:50_1_1"/>
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" title="GRAPH_3:func.8">AddNewEdge</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="graph_3.html#D7" target="_self" title="GRAPH_3:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E6:50_1_1"/>
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="graph_3.html#K8" title="GRAPH_3:func.8">AddNewEdge</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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