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<span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:117_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="117_1_1"><span class="kw">suppose </span></a><a NAME="E1:117_1_1"/><span class="lab"><font color="Green" title="E91">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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> </span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c2">u</font> =  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/><a NAME="E2:117_1_1"/>
 the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:117_1_1"><span class="lab"><font color="Green" title="E91">A1</font></span></a>, <a class="ref" href="chord.html#T64" target="_self" onmouseover="rs('chord/T64')" onmouseout="rh()">Th63</a></span>;<br/><span class="kw">hence </span><a NAME="E3:117_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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_2"><span class="kw">suppose </span></a><a NAME="E1:117_1_2"/><span class="lab"><font color="Green" title="E91">A2</font></span>: 
 not <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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> </span><br/><div class="add"><a NAME="E2:117_1_2"/><span class="kw">then </span>
 not <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a> 
 ;<br/><a NAME="E3:117_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp;  not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; <font color="Olive" title="b1">a</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>  &amp; <font color="Olive" title="b2">b</font> is  <a href="chord.html#V3" title="CHORD:attr.3">simplicial</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:117_1_2"><span class="lab"><font color="Green" title="E91">A2</font></span></a>, <a class="ref" href="chord.html#T102" target="_self" onmouseover="rs('chord/T102')" onmouseout="rh()">Th101</a></span>;<br/><span class="kw">hence </span><a NAME="E4:117_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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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