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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:34"/>
 <a href="sgraph1.html#G1" target="_self">SimpleGraphStruct</a>(# <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> <span class="p2">(<span class="default"><a href="sgraph1.html#K2" target="_self">TWOELEMENTSETS</a> <a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span> #) <a href="hidden.html#R2">in</a>  <a href="sgraph1.html#K3" target="_self">SIMPLEGRAPHS</a> <font color="Maroon">X</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="sgraph1.html#D9" target="_self">SGRAPH1:def 9</a><br/>

<b>thus </b><a NAME="E2:34"/>
for <font color="Olive">VV</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><br/> for <font color="Olive">EE</font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" target="_self">TWOELEMENTSETS</a> <font color="Olive">VV</font></span>)</span><br/> for <font color="Olive">nn</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">EEvn</font> being <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" target="_self">TWOELEMENTSETS</a> <span class="p2">(<span class="default"><font color="Olive">VV</font> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">nn</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>  st  <a href="sgraph1.html#G1" target="_self">SimpleGraphStruct</a>(# <font color="Olive">VV</font>,<font color="Olive">EE</font> #) <a href="hidden.html#R2">in</a>  <a href="sgraph1.html#K3" target="_self">SIMPLEGRAPHS</a> <font color="Maroon">X</font> &amp; <font color="Olive">nn</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; not <font color="Olive">nn</font> <a href="hidden.html#R2">in</a> <font color="Olive">VV</font> holds <br/> <a href="sgraph1.html#G1" target="_self">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><font color="Olive">VV</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">nn</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<font color="Olive">EEvn</font> #) <a href="hidden.html#R2">in</a>  <a href="sgraph1.html#K3" target="_self">SIMPLEGRAPHS</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E3:34"/>
for <font color="Olive">V</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><br/> for <font color="Olive">E</font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" target="_self">TWOELEMENTSETS</a> <font color="Olive">V</font></span>)</span><br/> for <font color="Olive">v1</font>, <font color="Olive">v2</font> being   <a href="hidden.html#M1">set</a>   st  <a href="sgraph1.html#G1" target="_self">SimpleGraphStruct</a>(# <font color="Olive">V</font>,<font color="Olive">E</font> #) <a href="hidden.html#R2">in</a>  <a href="sgraph1.html#K3" target="_self">SIMPLEGRAPHS</a> <font color="Maroon">X</font> &amp; <font color="Olive">v1</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> &amp; <font color="Olive">v2</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> &amp; <font color="Olive">v1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">v2</font> &amp; not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Olive">v1</font>,<font color="Olive">v2</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">E</font> holds <br/> ex <font color="Olive">v1v2</font> being <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" target="_self">TWOELEMENTSETS</a> <font color="Olive">V</font></span>)</span> st <br/>( <font color="Olive">v1v2</font> <a href="hidden.html#R1">=</a> <font color="Olive">E</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Olive">v1</font>,<font color="Olive">v2</font></span><a href="tarski.html#K2">}</a></span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sgraph1.html#G1" target="_self">SimpleGraphStruct</a>(# <font color="Olive">V</font>,<font color="Olive">v1v2</font> #) <a href="hidden.html#R2">in</a>  <a href="sgraph1.html#K3" target="_self">SIMPLEGRAPHS</a> <font color="Maroon">X</font> )
 <b>by </b><i/>;<br/>


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