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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:70"/>
<font color="Maroon">G</font> is <a href="glib_000.html#V4">trivial</a>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:70"/><i><font color="Green">E30</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">x</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/>
<b>let </b><font color="Maroon">u</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>, <font color="Maroon">v</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="chord.html#D6" target="_self">CHORD:def 6</a><br/>

<b>assume </b><a NAME="E4:70"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font> &amp; not <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 ;<br/>

<a NAME="E5:70"/>
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:70"/>
contradiction
 <b>by </b><i/>;<br/>


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