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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>assume </b><b>that </b><br/><a NAME="E1:94"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E2:94"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="chord.html#R1" target="_self">are_adjacent</a> 
 ;<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="E3:94"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">S</font> is <a href="chord.html#V4" target="_self">minimal</a>
 ;<br/>

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

<b>assume </b><a NAME="E4:94"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 ;<br/>

<b>assume </b><a NAME="E5:94"/>
not <font color="Maroon">T</font> is <a href="chord.html#V4" target="_self">minimal</a>
 ;<br/>

<b>then consider </b><font color="Maroon">H</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E7:94"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">T</font> &amp; <font color="Maroon">H</font> is    <a href="chord.html#M2" target="_self">VertexSeparator</a> of <font color="Maroon">b</font>,<font color="Maroon">a</font> )
 <b>by </b><i/>;<br/>
<a NAME="E8:94"/>
( <font color="Maroon">H</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">S</font> &amp; <font color="Maroon">H</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>, , , , </i>;<br/>
<b>hence </b><a NAME="E9:94"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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