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<b>let </b><font color="Maroon" title="c1">G1</font> be  non <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c3">G2</font> be   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">v</font>;<br/>





<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c3">G2</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> &amp;  ex <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  &amp; not <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G1</font> ) )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:62"/><i><font color="Green" title="E42">A2</font></i>: 
( <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  &amp; not <font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G1</font> )
 ;<br/>
<div><i><font color="Green" title="E43">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>assume </b><a NAME="E1:62_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font>
 ;<br/><a NAME="E2:62_1"/><b>then </b>
not <font color="Maroon" title="c5">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="c2">v</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="E3:62_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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">G1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">v</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#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E4:62_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#T50" title="GLIB_000:th.50">GLIB_000:50</a></i>;<br/></div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c5">v3</font> = <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>;<br/>
<a NAME="E5:62"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>
 
<b>by </b><i><a class="txt" href="glib_002.html#E3:62"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="glib_000.html#T70" title="GLIB_000:th.70">GLIB_000:70</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">v3'</font> = <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E4:62"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/>
<a NAME="E7:62"/><i><font color="Green" title="E44">A4</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c1">G1</font>
 
<b>by </b><i><a class="txt" href="glib_002.html#E3:62"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="glib_000.html#T70" title="GLIB_000:th.70">GLIB_000:70</a></i>;<br/>
<a NAME="E8:62"/><b>then </b><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G1</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="hs2(this)" href="javascript:()" title="62_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_2_1_1"/>
( <font color="Maroon" title="c7">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> or <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_1"><b>suppose </b></a><a NAME="E1:62_2_1_1_1"/>
<font color="Maroon" title="c7">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c9">v1'</font> = <font color="Maroon" title="c7">v1</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E4:62"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_2_1_1_1_1_1"/>
( <font color="Maroon" title="c8">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> or <font color="Maroon" title="c8">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:62_2_1_1_1_1_1_1"/>
<font color="Maroon" title="c8">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c10">v2'</font> = <font color="Maroon" title="c8">v2</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E4:62"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">W'</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c3">G2</font><b> such that </b><br/><a NAME="E4:62_2_1_1_1_1_1_1"/><i><font color="Green" title="E46">A6</font></i>: 
<font color="Maroon" title="c11">W'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c9">v1'</font>,<font color="Maroon" title="c10">v2'</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:62"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">W</font> = <font color="Maroon" title="c11">W'</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><a NAME="E6:62_2_1_1_1_1_1_1"/>
<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">v1</font>,<font color="Maroon" title="c8">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E4:62_2_1_1_1_1_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>hence </b><a NAME="E7:62_2_1_1_1_1_1_1"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:62_2_1_1_1_1_1_2"/><i><font color="Green" title="E46">A7</font></i>: 
<font color="Maroon" title="c8">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c10">W'</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c3">G2</font><b> such that </b><br/><a NAME="E3:62_2_1_1_1_1_1_2"/><i><font color="Green" title="E47">A8</font></i>: 
<font color="Maroon" title="c10">W'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c9">v1'</font>,<font color="Maroon" title="c6">v3'</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:62"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">W</font> = <font color="Maroon" title="c10">W'</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><a NAME="E5:62_2_1_1_1_1_1_2"/>
<font color="Maroon" title="c11">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:62_2_1_1_1_1_1_2"><i><font color="Green" title="E47">A8</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><a NAME="E6:62_2_1_1_1_1_1_2"/><b>then </b>
( <font color="Maroon" title="c11">W</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> &amp; <font color="Maroon" title="c11">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font> )
 <b>by </b><i><a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E7:62_2_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c11">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c4">e</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E8:62"><i><font color="Green" title="E45">A5</font></i></a>, <a class="txt" href="glib_002.html#E1:62_2_1_1_1_1_1_2"><i><font color="Green" title="E46">A7</font></i></a>, <a class="ref" href="glib_001.html#T64" title="GLIB_001:th.64">GLIB_001:64</a></i>;<br/><b>hence </b><a NAME="E8:62_2_1_1_1_1_1_2"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:62_2_1_1_1"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_2"><b>suppose </b></a><a NAME="E1:62_2_1_1_2"/><i><font color="Green" title="E46">A9</font></i>: 
<font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:62_2_1_1_2_1_1"/>
( <font color="Maroon" title="c8">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font> or <font color="Maroon" title="c8">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="62_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:62_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c8">v2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c9">v2'</font> = <font color="Maroon" title="c8">v2</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E4:62"><i><font color="Green" title="E43">A3</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c10">W1</font> = <font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">e</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font></span>)</span>;<br/><a NAME="E3:62_2_1_1_2_1_1_1"/><i><font color="Green" title="E47">A10</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">e</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E7:62"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="glib_002.html#E1:62_2_1_1_2"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="glib_001.html#T16" title="GLIB_001:th.16">GLIB_001:16</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">W2'</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c3">G2</font><b> such that </b><br/><a NAME="E5:62_2_1_1_2_1_1_1"/><i><font color="Green" title="E48">A11</font></i>: 
<font color="Maroon" title="c11">W2'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c6">v3'</font>,<font color="Maroon" title="c9">v2'</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:62"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">W2</font> = <font color="Maroon" title="c11">W2'</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><a NAME="E7:62_2_1_1_2_1_1_1"/><i><font color="Green" title="E49">A12</font></i>: 
<font color="Maroon" title="c12">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c8">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E5:62_2_1_1_2_1_1_1"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>take </b><font color="Maroon" title="c13">W</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c4">e</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c4">e</font></span>)</span></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c12">W2</font>;<br/><b>thus </b><a NAME="E8:62_2_1_1_2_1_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">v1</font>,<font color="Maroon" title="c8">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:62_2_1_1_2_1_1_1"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="glib_002.html#E7:62_2_1_1_2_1_1_1"><i><font color="Green" title="E49">A12</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="62_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:62_2_1_1_2_1_1_2"/><i><font color="Green" title="E47">A13</font></i>: 
<font color="Maroon" title="c8">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c9">W</font> = <font color="Maroon" title="c1">G1</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font>;<br/><b>thus </b><a NAME="E2:62_2_1_1_2_1_1_2"/>
<font color="Maroon" title="c9">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:62_2_1_1_2"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="glib_002.html#E1:62_2_1_1_2_1_1_2"><i><font color="Green" title="E47">A13</font></i></a>, <a class="ref" href="glib_001.html#T14" title="GLIB_001:th.14">GLIB_001:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:62_2_1_1_2"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E2:62_2"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:62"/>
<font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/>


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