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<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V4">trivial</a> <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:77_1"/>
<font color="Maroon">G</font> <a href="chord.html#K2" target="_self">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:77_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="chord.html#K2" target="_self">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>consider </b><font color="Maroon">u</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E5:77_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font>
 <b>and </b><br/><a NAME="E6:77_1"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>and </b><br/><a NAME="E7:77_1"/>
 ex <font color="Olive">v1</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">v1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">u</font>,<font color="Olive">v1</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">w</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E9:77_1"/><i><font color="Green">E53</font></i>: 
 <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">w</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#T25">GLIB_000:25</a></i>;<br/><a NAME="E10:77_1"/>
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E11:77_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:77"/>
<font color="Maroon">v</font> is <a href="chord.html#V3" target="_self">simplicial</a>
 <b>by </b><i/>;<br/>


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