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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:121"/><i><font color="Green" title="E93">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">S</font> be    <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>;<br/>

<b>assume </b><a NAME="E2:121"/><i><font color="Green" title="E94">A2</font></i>: 
<font color="Maroon" title="c4">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">H</font> be   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c4">S</font>;<br/><b>let </b><font color="Maroon" title="c6">a1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c5">H</font>;<br/>



<b>assume </b><a NAME="E3:121"/><i><font color="Green" title="E95">A3</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a1</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:121"/><i><font color="Green" title="E96">A4</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">S</font>
 <b>and </b><br/><a NAME="E5:121"/><i><font color="Green" title="E97">A5</font></i>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">S</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c9">c</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E7:121"/><i><font color="Green" title="E98">A6</font></i>: 
<font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">H</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c6">a1</font>
 <b>and </b><br/><a NAME="E8:121"/><i><font color="Green" title="E99">A7</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">S</font> holds <br/><font color="Maroon" title="c9">c</font>,<font color="Olive" title="b1">x</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="chord.html#E1:121"><i><font color="Green" title="E93">A1</font></i></a>, <a class="txt" href="chord.html#E2:121"><i><font color="Green" title="E94">A2</font></i></a>, <a class="txt" href="chord.html#E3:121"><i><font color="Green" title="E95">A3</font></i></a>, <a class="ref" href="chord.html#T100" target="_self" title="CHORD:th.100">Th100</a></i>;<br/>
<a NAME="E9:121"/>
( <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c7">x</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; <font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c8">y</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )
 
<b>by </b><i><a class="txt" href="chord.html#E4:121"><i><font color="Green" title="E96">A4</font></i></a>, <a class="txt" href="chord.html#E5:121"><i><font color="Green" title="E97">A5</font></i></a>, <a class="txt" href="chord.html#E8:121"><i><font color="Green" title="E99">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:121"/>
 ex <font color="Olive" title="b1">c</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">H</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c6">a1</font> &amp; <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c7">x</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  &amp; <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c8">y</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )
 <b>by </b><i><a class="txt" href="chord.html#E7:121"><i><font color="Green" title="E98">A6</font></i></a></i>;<br/>


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