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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">a</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>, <font color="Maroon">b</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="chord.html#M2" target="_self">VertexSeparator</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>





<b>assume </b><a NAME="E1:92"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:92_1"/>
not <font color="Maroon">S</font> is <a href="chord.html#V4" target="_self">minimal</a>
 ;<br/><b>then consider </b><font color="Maroon">T</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:92_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">T</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">S</font> &amp; <font color="Maroon">T</font> is    <a href="chord.html#M2" target="_self">VertexSeparator</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:92_1"/>
contradiction
 <b>by </b><i><a class="ref" href="chord.html#T17" target="_self">Th17</a>, , <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:92"/>
<font color="Maroon">S</font> is <a href="chord.html#V4" target="_self">minimal</a>
 ;<br/>


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