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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:251"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="251_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="251_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:251_1_1"/>
( <font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font> or  not <font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="251_1_1_1"><b>suppose </b></a><a NAME="E1:251_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font>
 ;<br/><div class="add"><a NAME="E2:251_1_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/><b>thus </b><font color="Maroon">G1</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font> = 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">G2</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font>
<b>by </b><i><a class="txt" href="glib_001.html#E58"><i><font color="Green">Lemma163</font></i></a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="251_1_1_2"><b>suppose </b></a><a NAME="E1:251_1_1_2"/><i><font color="Green">E43</font></i>: 
not <font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font>
 ;<br/><div class="add"><a NAME="E2:251_1_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
not <font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/><b>thus </b><font color="Maroon">G1</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font> = 
<font color="Maroon">G1</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G1</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">G2</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, <a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>
<br/>.= 
<font color="Maroon">G2</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font>
<b>by </b><i><a class="txt" href="glib_001.html#E58"><i><font color="Green">Lemma163</font></i></a>, </i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:251"/>
<font color="Maroon">G1</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <font color="Maroon">x</font>,<font color="Maroon">e</font>,<font color="Maroon">y</font>
 ;<br/>


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