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



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">u</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>
 ;<br/><b>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="E3:59_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x</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="Maroon">x</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 <b>by </b><i><a class="txt" href="chord.html#E15"><i><font color="Green">Lemma49</font></i></a>, <a class="ref" href="chord.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:59_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:59_1"/>
( <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font> &amp; <font color="Maroon">v</font>,<font color="Maroon">u</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 <b>by </b><i><a class="txt" href="chord.html#E15"><i><font color="Green">Lemma49</font></i></a>, , <a class="ref" href="chord.html#T11" target="_self">Th11</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:59"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font> &amp; <font color="Maroon">v</font>,<font color="Maroon">u</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 ;<br/>

<a NAME="E3:59"/><b>then </b>
( 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> &amp; <font color="Maroon">v</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>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:59"/>
<font color="Maroon">u</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="txt" href="chord.html#E15"><i><font color="Green">Lemma49</font></i></a></i>;<br/>


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