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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><a NAME="E1:89"/><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>let </b><font color="Maroon">G2</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">a2</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>, <font color="Maroon">b2</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E2:89"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E3:89"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<b>set </b><font color="Maroon">A</font> = <font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a2</font>;<br/>
<b>set </b><font color="Maroon">B</font> = <font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">b2</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:89_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">b2</font></span>)</span>
 ;<br/><a NAME="E2:89_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">W1</font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font><b> such that </b><br/><a NAME="E4:89_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">W1</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">a2</font>,<font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5">GLIB_002:def 5</a></i>;<br/><a NAME="E5:89_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">b2</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">rW2</font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font><b> such that </b><br/><a NAME="E7:89_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">rW2</font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">b2</font>,<font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5">GLIB_002:def 5</a></i>;<br/><b>set </b><font color="Maroon">W2</font> = <font color="Maroon">rW2</font> <a href="glib_001.html#K6">.reverse()</a> ;<br/><b>set </b><font color="Maroon">W</font> = <font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">rW2</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span>;<br/><a NAME="E8:89_1"/>
<font color="Maroon">rW2</font> <a href="glib_001.html#K6">.reverse()</a>  <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">x</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, <a class="ref" href="glib_001.html#T24">GLIB_001:24</a></i>;<br/><a NAME="E9:89_1"/><b>then </b>
<font color="Maroon">W1</font> <a href="glib_001.html#K7">.append</a> <span class="p1">(<span class="default"><font color="Maroon">rW2</font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">a2</font>,<font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="chord.html#T17" target="_self">Th17</a>, <a class="ref" href="glib_001.html#T32">GLIB_001:32</a></i>;<br/><b>hence </b><a NAME="E10:89_1"/>
contradiction
 <b>by </b><i>, , , <a class="txt" href="chord.html#E7:89_1"><i><font color="Green">E66</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:89"/>
<span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">a2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">G2</font> <a href="glib_002.html#K1">.reachableFrom</a> <font color="Maroon">b2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>


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