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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">W1A</font>, <font color="Maroon" title="c4">W1B</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c5">W2A</font>, <font color="Maroon" title="c6">W2B</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font>;<br/>







<b>assume </b><a NAME="E1:166"/><i><font color="Green" title="E115">A1</font></i>: 
( <font color="Maroon" title="c3">W1A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">W2A</font> &amp; <font color="Maroon" title="c4">W1B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">W2B</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="166_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:166_1_1"/>
( <font color="Maroon" title="c3">W1A</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="c4">W1B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  or <font color="Maroon" title="c3">W1A</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">W1B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1_1"><b>suppose </b></a><a NAME="E1:166_1_1_1"/><i><font color="Green" title="E116">A2</font></i>: 
<font color="Maroon" title="c3">W1A</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="c4">W1B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
 ;<br/><div class="add"><a NAME="E2:166_1_1_1"/><b>then </b><i><font color="Green" title="E117">A3</font></i>: 
<font color="Maroon" title="c5">W2A</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="c6">W2B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E1:166"><i><font color="Green" title="E115">A1</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c3">W1A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c4">W1B</font> = 
<font color="Maroon" title="c3">W1A</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c4">W1B</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:166_1_1_1"><i><font color="Green" title="E116">A2</font></i></a>, <a class="ref" href="glib_001.html#D10" target="_self" title="GLIB_001:def.10">Def10</a></i>
<br/>.= 
<font color="Maroon" title="c5">W2A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c6">W2B</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:166"><i><font color="Green" title="E115">A1</font></i></a>, <a class="txt" href="glib_001.html#E2:166_1_1_1"><i><font color="Green" title="E117">A3</font></i></a>, <a class="ref" href="glib_001.html#D10" target="_self" title="GLIB_001:def.10">Def10</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="166_1_1_2"><b>suppose </b></a><a NAME="E1:166_1_1_2"/><i><font color="Green" title="E116">A4</font></i>: 
<font color="Maroon" title="c3">W1A</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">W1B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
 ;<br/><div class="add"><a NAME="E2:166_1_1_2"/><b>then </b><i><font color="Green" title="E117">A5</font></i>: 
<font color="Maroon" title="c5">W2A</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">W2B</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E1:166"><i><font color="Green" title="E115">A1</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c3">W1A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c4">W1B</font> = 
<font color="Maroon" title="c5">W2A</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:166"><i><font color="Green" title="E115">A1</font></i></a>, <a class="txt" href="glib_001.html#E1:166_1_1_2"><i><font color="Green" title="E116">A4</font></i></a>, <a class="ref" href="glib_001.html#D10" target="_self" title="GLIB_001:def.10">Def10</a></i>
<br/>.= 
<font color="Maroon" title="c5">W2A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c6">W2B</font>
<b>by </b><i><a class="txt" href="glib_001.html#E2:166_1_1_2"><i><font color="Green" title="E117">A5</font></i></a>, <a class="ref" href="glib_001.html#D10" target="_self" title="GLIB_001:def.10">Def10</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:166"/>
<font color="Maroon" title="c3">W1A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c4">W1B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">W2A</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c6">W2B</font>
 ;<br/>


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