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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">S</font> be    <a href="hidden.html#M1">set</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>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:57_1"/>
<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> <font color="Maroon">S</font>
 ;<br/><b>then consider </b><font color="Maroon">t</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:57_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>and </b><br/><a NAME="E4:57_1"/><i><font color="Green">E33</font></i>: 
( not <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp;  ex <font color="Olive">v</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">t</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) )
 ;<br/><b>thus </b><a NAME="E5:57_1"/>
( not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp;  ex <font color="Olive">v</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">u</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) )
 <b>by </b><i><a class="ref" href="chord.html#T12" target="_self">Th12</a>, <a class="ref" href="chord.html#T13" target="_self">Th13</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:57"/>
( not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp;  ex <font color="Olive">v</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">u</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) )
 ;<br/>

<b>hence </b><a NAME="E3:57"/>
<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> <font color="Maroon">S</font>
 ;<br/>


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