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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">g</font> being   <a href="sgraph1.html#M1" title="SGRAPH1:mode.1">SimpleGraph</a> of <font color="Maroon" title="c1">X</font> holds <br/> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Olive" title="b1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">g</font> )</span><br/><b>let </b><font color="Maroon" title="c2">g</font> be    <a href="sgraph1.html#M1" title="SGRAPH1:mode.1">SimpleGraph</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font> )</span><br/>



<a NAME="E1:24"/>
<font color="Maroon" title="c2">g</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="sgraph1.html#K3" title="SGRAPH1:func.3">SIMPLEGRAPHS</a> <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/>
<b>then consider </b><font color="Maroon" title="c3">v</font> being  <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>, <font color="Maroon" title="c4">e</font> being  <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> <font color="Maroon" title="c3">v</font></span>)</span><b> such that </b><br/><a NAME="E3:24"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">e</font> #)
 <b>by </b><i><a class="ref" href="sgraph1.html#T21" target="_self" title="SGRAPH1:th.21">Th21</a></i>;<br/>
<b>thus </b><a NAME="E4:24"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="#E3:24"><i><font color="Green" title="E15">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font></span><br/>

<b>thus </b><a NAME="E5:24"/>
the <a href="sgraph1.html#U1" title="SGRAPH1:sel.1">SEdges</a> of <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">g</font>
 ; <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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