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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:123_1"/>
( <font color="Maroon" title="c1">G</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> or  not <font color="Maroon" title="c1">G</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1_1"><b>suppose </b></a><a NAME="E1:123_1_1"/><i><font color="Green" title="E95">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c2">u</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/><a NAME="E3:123_1_1"/>
<font color="Maroon" title="c2">u</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 <b>by </b><i><a class="txt" href="chord.html#E1:123_1_1"><i><font color="Green" title="E95">A1</font></i></a>, <a class="ref" href="chord.html#T64" target="_self" title="CHORD:th.64">Th64</a></i>;<br/><b>hence </b><a NAME="E4:123_1_1"/>
 ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">v</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1_2"><b>suppose </b></a><a NAME="E1:123_1_2"/><i><font color="Green" title="E95">A2</font></i>: 
not <font color="Maroon" title="c1">G</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 ;<br/><div class="add"><a NAME="E2:123_1_2"/><b>then </b><i><font color="Green" title="E96">A3</font></i>: 
not <font color="Maroon" title="c1">G</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 <b>by </b><i><a class="ref" href="chord.html#T61" target="_self" title="CHORD:th.61">Th61</a></i>;<br/><b>consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:123_1_2"/><i><font color="Green" title="E97">A4</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; <font color="Maroon" title="c2">a</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> &amp; <font color="Maroon" title="c3">b</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> )
 <b>by </b><i><a class="txt" href="chord.html#E1:123_1_2"><i><font color="Green" title="E95">A2</font></i></a>, <a class="txt" href="chord.html#E2:123_1_2"><i><font color="Green" title="E96">A3</font></i></a>, <a class="ref" href="chord.html#T102" target="_self" title="CHORD:th.102">Th102</a></i>;<br/><b>thus </b><a NAME="E5:123_1_2"/>
 ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">v</font> is <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>
 <b>by </b><i><a class="txt" href="chord.html#E4:123_1_2"><i><font color="Green" title="E97">A4</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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