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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:93"/><span class="lab"><font color="Green" title="E77">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:93"/><span class="lab"><font color="Green" title="E78">A2</font></span>: 
 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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E3:93"/><span class="lab"><font color="Green" title="E79">A3</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E4:93"/><span class="lab"><font color="Green" title="E80">A4</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E5:93"/>
 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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E7:93"/><span class="lab"><font color="Green" title="E81">A5</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:93"/><span class="lab"><font color="Green" title="E82">A6</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D9" target="_self" title="CHORD:def.9">Def9</a></span>;<br/>
<a NAME="E9:93"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E77">A1</font></span></a>, <a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E78">A2</font></span></a>, <a class="txt" href="#E8:93"><span class="lab"><font color="Green" title="E82">A6</font></span></a>, <a class="ref" href="chord.html#T70" target="_self" title="CHORD:th.70">Th70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:93"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:93"><span class="lab"><font color="Green" title="E79">A3</font></span></a>, <a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E80">A4</font></span></a>, <a class="txt" href="#E7:93"><span class="lab"><font color="Green" title="E81">A5</font></span></a>, <a class="ref" href="chord.html#D9" target="_self" title="CHORD:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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