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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">E</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> <font color="Maroon" title="c2">V</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c5">Evn</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">n</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>;<br/>









<b>set </b><font color="Maroon" title="c6">g</font> =  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">E</font> #);<br/>
<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E17">A1</font></i>: 
(  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">E</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sgraph1.html#K3" title="SGRAPH1:func.3">SIMPLEGRAPHS</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; not <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">g</font> =  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">E</font> #) as    <a href="sgraph1.html#M1" title="SGRAPH1:mode.1">SimpleGraph</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="sgraph1.html#D7" target="_self" title="SGRAPH1:def.7">Def7</a></i>;<br/>
<a NAME="E3:31"/>
<font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">g</font>
 
;<br/>
<a NAME="E4:31"/><b>then </b>
<font color="Maroon" title="c2">V</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="sgraph1.html#T27" target="_self" title="SGRAPH1:th.27">Th27</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
<font color="Maroon" title="c2">V</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"><font color="Maroon" title="c4">n</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="sgraph1.html#E1:31"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="sgraph1.html#E10"><i><font color="Green" title="E4">Lm2</font></i></a>, <a class="ref" href="finset_1.html#T14" title="FINSET_1:th.14">FINSET_1:14</a></i>;<br/>
<b>hence </b><a NAME="E6:31"/>
 <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">n</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<font color="Maroon" title="c5">Evn</font> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sgraph1.html#K3" title="SGRAPH1:func.3">SIMPLEGRAPHS</a> <font color="Maroon" title="c1">X</font>
 ;<br/>


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