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<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2">finite</a> <a href="chord.html#V6" target="_self">chordal</a> <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><a NAME="E1:121"/><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> &amp; 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="E2:121"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">S</font> is <a href="chord.html#V4" target="_self">minimal</a>
 ;<br/>

<b>let </b><font color="Maroon">H</font> be   <a href="glib_000.html#NM7">removeVertices</a> of <font color="Maroon">G</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">H</font>;<br/>



<b>assume </b><a NAME="E3:121"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>, <font color="Maroon">y</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="E4:121"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E5:121"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>consider </b><font color="Maroon">c</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E7:121"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a1</font>
 <b>and </b><br/><a NAME="E8:121"/><i><font color="Green">E67</font></i>: 
for <font color="Olive">x</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">c</font>,<font color="Olive">x</font> <a href="chord.html#R1" target="_self">are_adjacent</a> 
 <b>by </b><i>, , , </i>;<br/>
<a NAME="E9:121"/>
( <font color="Maroon">c</font>,<font color="Maroon">x</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">y</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E10:121"/>
 ex <font color="Olive">c</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a1</font> &amp; <font color="Olive">c</font>,<font color="Maroon">x</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  &amp; <font color="Olive">c</font>,<font color="Maroon">y</font> <a href="chord.html#R1" target="_self">are_adjacent</a>  )
 <b>by </b><i/>;<br/>


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