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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>;<br/><b>let </b><font color="Maroon" title="c2">G0</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">x</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>let </b><font color="Maroon" title="c5">G1</font> be   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c3">S</font>;<br/><b>let </b><font color="Maroon" title="c6">G2</font> be   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:64"/><i><font color="Green" title="E51">A1</font></i>: 
<font color="Maroon" title="c5">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>and </b><br/><a NAME="E2:64"/><i><font color="Green" title="E52">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c5">G1</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon" title="c7">u</font>, <font color="Maroon" title="c8">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c6">G2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a><br/>

<b>reconsider </b><font color="Maroon" title="c9">Sx</font> = <font color="Maroon" title="c3">S</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span> ;<br/>
<a NAME="E4:64"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c6">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Sx</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/>
<a NAME="E5:64"/><b>then </b><i><font color="Green" title="E53">A3</font></i>: 
( ( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> or <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ) &amp; ( <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> or <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E6:64"/>
<font color="Maroon" title="c3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">Sx</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E7:64"/><b>then </b><i><font color="Green" title="E54">A4</font></i>: 
<font color="Maroon" title="c5">G1</font> is   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c6">G2</font>,<font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="ref" href="chord.html#T30" target="_self" title="CHORD:th.30">Th30</a></i>;<br/>
<a NAME="E8:64"/><i><font color="Green" title="E55">A5</font></i>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c5">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">xs</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="E10:64"/><i><font color="Green" title="E56">A6</font></i>: 
<font color="Maroon" title="c10">xs</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 <b>and </b><br/><a NAME="E11:64"/><i><font color="Green" title="E57">A7</font></i>: 
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">xs</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="chord.html#E2:64"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="chord.html#T50" target="_self" title="CHORD:th.50">Th50</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E13:64"/><i><font color="Green" title="E58">A8</font></i>: 
<font color="Maroon" title="c11">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="chord.html#E11:64"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="chord.html#D3" target="_self" title="CHORD:def.3">Def3</a></i>;<br/>
<a NAME="E14:64"/><i><font color="Green" title="E59">A9</font></i>: 
<font color="Maroon" title="c11">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="chord.html#E13:64"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="glib_000.html#T17" title="GLIB_000:th.17">GLIB_000:17</a></i>;<br/>
<a NAME="E15:64"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E16:64"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Sx</font> &amp; <font color="Maroon" title="c10">xs</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Sx</font> )
 
<b>by </b><i><a class="txt" href="chord.html#E10:64"><i><font color="Green" title="E56">A6</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E17:64"/><b>then </b><i><font color="Green" title="E60">A10</font></i>: 
<font color="Maroon" title="c11">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">G2</font>
 
<b>by </b><i><a class="txt" href="chord.html#E14:64"><i><font color="Green" title="E59">A9</font></i></a>, <a class="ref" href="chord.html#T19" target="_self" title="CHORD:th.19">Th19</a></i>;<br/>
<a NAME="E18:64"/><b>then </b><i><font color="Green" title="E61">A11</font></i>: 
<font color="Maroon" title="c11">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c6">G2</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T17" title="GLIB_000:th.17">GLIB_000:17</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:64_1"/>
( ( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> ) or ( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> ) or ( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> ) or ( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> ) )
 </span><b>by </b><i><a class="txt" href="chord.html#E5:64"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1"><b>suppose </b></a><a NAME="E1:64_1_1"/><i><font color="Green" title="E62">A12</font></i>: 
( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> )
 ;<br/><div class="add"><a NAME="E2:64_1_1"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c5">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c5">G1</font><b> such that </b><br/><a NAME="E4:64_1_1"/><i><font color="Green" title="E63">A13</font></i>: 
<font color="Maroon" title="c12">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E1:64"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="chord.html#E1:64_1_1"><i><font color="Green" title="E62">A12</font></i></a>, <a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">W</font> = <font color="Maroon" title="c12">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c6">G2</font> <b>by </b><i><a class="txt" href="chord.html#E7:64"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><b>take </b>
<font color="Maroon" title="c13">W</font>
;<br/><b>thus </b><a NAME="E6:64_1_1"/>
<font color="Maroon" title="c13">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E4:64_1_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_2"><b>suppose </b></a><a NAME="E1:64_1_2"/><i><font color="Green" title="E62">A14</font></i>: 
( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c5">G1</font><b> such that </b><br/><a NAME="E3:64_1_2"/><i><font color="Green" title="E63">A15</font></i>: 
<font color="Maroon" title="c12">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c10">xs</font>
 <b>by </b><i><a class="txt" href="chord.html#E10:64"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="chord.html#E8:64"><i><font color="Green" title="E55">A5</font></i></a>, <a class="txt" href="chord.html#E1:64"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">W</font> = <font color="Maroon" title="c12">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c6">G2</font> <b>by </b><i><a class="txt" href="chord.html#E7:64"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><b>take </b><font color="Maroon" title="c14">WW</font> = <font color="Maroon" title="c13">W</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c11">e</font>,<font color="Maroon" title="c4">x</font></span>)</span>;<br/><a NAME="E5:64_1_2"/><i><font color="Green" title="E64">A16</font></i>: 
<font color="Maroon" title="c13">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c10">xs</font>
 <b>by </b><i><a class="txt" href="chord.html#E3:64_1_2"><i><font color="Green" title="E63">A15</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><a NAME="E6:64_1_2"/>
<font color="Maroon" title="c6">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c11">e</font>,<font color="Maroon" title="c4">x</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="chord.html#E17:64"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="glib_001.html#T16" title="GLIB_001:th.16">GLIB_001:16</a></i>;<br/><b>hence </b><a NAME="E7:64_1_2"/>
<font color="Maroon" title="c14">WW</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E1:64_1_2"><i><font color="Green" title="E62">A14</font></i></a>, <a class="txt" href="chord.html#E5:64_1_2"><i><font color="Green" title="E64">A16</font></i></a>, <a class="ref" href="glib_001.html#T32" title="GLIB_001:th.32">GLIB_001:32</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_3"><b>suppose </b></a><a NAME="E1:64_1_3"/><i><font color="Green" title="E62">A17</font></i>: 
( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c12">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c5">G1</font><b> such that </b><br/><a NAME="E3:64_1_3"/><i><font color="Green" title="E63">A18</font></i>: 
<font color="Maroon" title="c12">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E10:64"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="chord.html#E8:64"><i><font color="Green" title="E55">A5</font></i></a>, <a class="txt" href="chord.html#E1:64"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">W</font> = <font color="Maroon" title="c12">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c6">G2</font> <b>by </b><i><a class="txt" href="chord.html#E7:64"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><b>take </b><font color="Maroon" title="c14">WW</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c11">e</font>,<font color="Maroon" title="c10">xs</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c13">W</font>;<br/><a NAME="E5:64_1_3"/><i><font color="Green" title="E64">A19</font></i>: 
<font color="Maroon" title="c13">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c10">xs</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E3:64_1_3"><i><font color="Green" title="E63">A18</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><a NAME="E6:64_1_3"/>
<font color="Maroon" title="c6">G2</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c11">e</font>,<font color="Maroon" title="c10">xs</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c10">xs</font>
 <b>by </b><i><a class="txt" href="chord.html#E18:64"><i><font color="Green" title="E61">A11</font></i></a>, <a class="ref" href="glib_001.html#T16" title="GLIB_001:th.16">GLIB_001:16</a></i>;<br/><b>hence </b><a NAME="E7:64_1_3"/>
<font color="Maroon" title="c14">WW</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="txt" href="chord.html#E1:64_1_3"><i><font color="Green" title="E62">A17</font></i></a>, <a class="txt" href="chord.html#E5:64_1_3"><i><font color="Green" title="E64">A19</font></i></a>, <a class="ref" href="glib_001.html#T32" title="GLIB_001:th.32">GLIB_001:32</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_4"><b>suppose </b></a><a NAME="E1:64_1_4"/>
( <font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> )
 ;<br/><div class="add"><a NAME="E2:64_1_4"/><b>then </b>
<font color="Maroon" title="c6">G2</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">u</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 <b>by </b><i><a class="ref" href="glib_001.html#T14" title="GLIB_001:th.14">GLIB_001:14</a></i>;<br/><b>hence </b><a NAME="E3:64_1_4"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c6">G2</font> st <font color="Olive">b<sub>1</sub></font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c8">v</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
