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<b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> : ( not <font color="Olive">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="Olive">u</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) ) </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:55_1_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> : ( not <font color="Olive">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="Olive">u</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) ) </span>}</span> 
 ;<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="E3:55_1_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E4:55_1_1_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#T11" target="_self">Th11</a></i>;<br/><b>thus </b><a NAME="E5:55_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="chord.html#T12" target="_self">Th12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:55_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">u</font> where <font color="Olive">u</font> is   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> : ( not <font color="Olive">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="Olive">u</font>,<font color="Olive">v</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  ) ) </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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