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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</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">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  holds <br/>for <font color="Olive" title="b3">S</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>  st <font color="Olive" title="b3">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> holds <br/>for <font color="Olive" title="b4">T</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>  st <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">T</font> holds <br/><font color="Olive" title="b4">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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>  implies for <font color="Olive" title="b1">S</font> being   <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>  st <font color="Olive" title="b1">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> holds <br/>for <font color="Olive" title="b2">T</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>  st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">T</font> holds <br/><font color="Olive" title="b2">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:94"/><i><font color="Green" title="E77">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>
 <b>and </b><br/><a NAME="E2:94"/><i><font color="Green" title="E78">A2</font></i>: 
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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being   <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>  st <font color="Olive" title="b1">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> holds <br/>for <font color="Olive" title="b2">T</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>  st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">T</font> holds <br/><font color="Olive" title="b2">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> implies for <font color="Olive" title="b1">T</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>  st <font color="Maroon" title="c4">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">T</font> holds <br/><font color="Olive" title="b1">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> )</span><br/>

<b>assume </b><a NAME="E3:94"/><i><font color="Green" title="E79">A3</font></i>: 
<font color="Maroon" title="c4">S</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T</font> being   <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>  st <font color="Maroon" title="c4">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">T</font> holds <br/><font color="Olive" title="b1">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a></span><br/>

<b>let </b><font color="Maroon" title="c5">T</font> be    <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T</font> implies <font color="Maroon" title="c5">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a> )</span><br/>

<b>assume </b><a NAME="E4:94"/><i><font color="Green" title="E80">A4</font></i>: 
<font color="Maroon" title="c4">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a></span><br/>

<b>assume </b><a NAME="E5:94"/>
not <font color="Maroon" title="c5">T</font> is <a href="chord.html#V4" title="CHORD:attr.4">minimal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c6">H</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">T</font><b> such that </b><br/><a NAME="E7:94"/><i><font color="Green" title="E81">A5</font></i>: 
( <font color="Maroon" title="c6">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">T</font> &amp; <font color="Maroon" title="c6">H</font> is    <a href="chord.html#M2" title="CHORD:mode.2">VertexSeparator</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 <b>by </b><i><a class="ref" href="chord.html#D9" target="_self" title="CHORD:def.9">Def9</a></i>;<br/>
<a NAME="E8:94"/>
( <font color="Maroon" title="c6">H</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">S</font> &amp; <font color="Maroon" title="c6">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">S</font> &amp; <font color="Maroon" title="c6">H</font> is    <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> )
 
<b>by </b><i><a class="txt" href="chord.html#E1:94"><i><font color="Green" title="E77">A1</font></i></a>, <a class="txt" href="chord.html#E2:94"><i><font color="Green" title="E78">A2</font></i></a>, <a class="txt" href="chord.html#E4:94"><i><font color="Green" title="E80">A4</font></i></a>, <a class="txt" href="chord.html#E7:94"><i><font color="Green" title="E81">A5</font></i></a>, <a class="ref" href="chord.html#T70" target="_self" title="CHORD:th.70">Th70</a></i>;<br/>
<b>hence </b><a NAME="E9:94"/>
contradiction
 <b>by </b><i><a class="txt" href="chord.html#E3:94"><i><font color="Green" title="E79">A3</font></i></a>, <a class="ref" href="chord.html#D9" target="_self" title="CHORD:def.9">Def9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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