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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c3">v1</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="c4">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>;<br/>







<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E43">A1</font></i>: 
( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:72_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c3">v1</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">W</font> being   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c1">G1</font><b> such that </b><br/><a NAME="E3:72_1_1"/><i><font color="Green" title="E44">A2</font></i>: 
<font color="Maroon" title="c6">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:72"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="glib_002.html#D6" target="_self" title="GLIB_002:def.6">Def6</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">W2</font> = <font color="Maroon" title="c6">W</font> as   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c2">G2</font> <b>by </b><i><a class="txt" href="glib_002.html#E1:72"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="glib_001.html#T182" title="GLIB_001:th.182">GLIB_001:182</a>, <a class="ref" href="glib_001.html#T180" title="GLIB_001:th.180">GLIB_001:180</a></i>;<br/><a NAME="E5:72_1_1"/>
<font color="Maroon" title="c7">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:72_1_1"><i><font color="Green" title="E44">A2</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="E6:72_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c4">v2</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D6" target="_self" title="GLIB_002:def.6">Def6</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:72_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c4">v2</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">W</font> being   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E4:72_1"/><i><font color="Green" title="E44">A3</font></i>: 
<font color="Maroon" title="c6">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:72"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="glib_002.html#D6" target="_self" title="GLIB_002:def.6">Def6</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">W2</font> = <font color="Maroon" title="c6">W</font> as   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="glib_002.html#E1:72"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="glib_001.html#T182" title="GLIB_001:th.182">GLIB_001:182</a>, <a class="ref" href="glib_001.html#T180" title="GLIB_001:th.180">GLIB_001:180</a></i>;<br/><a NAME="E6:72_1"/>
<font color="Maroon" title="c7">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E4:72_1"><i><font color="Green" title="E44">A3</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="E7:72_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c3">v1</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D6" target="_self" title="GLIB_002:def.6">Def6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:72"/>
<font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K2" title="GLIB_002:func.2">.reachableDFrom</a> <font color="Maroon" title="c4">v2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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