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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">W1</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>









<b>assume </b><a NAME="E1:170"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="170_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="170_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:170_1_1"/>
( ( not <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> &amp; not <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> ) or <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> or <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> or  not <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> or  not <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="170_1_1_1"><b>suppose </b></a><a NAME="E1:170_1_1_1"/><i><font color="Green">E40</font></i>: 
( not <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> &amp; not <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">W1</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> = 
<font color="Maroon">m</font>,<font color="Maroon">n</font> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">W2</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">W2</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="170_1_1_2"><b>suppose </b></a><a NAME="E1:170_1_1_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> or <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> or  not <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> or  not <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">W1</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> = 
<font color="Maroon">W2</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">W2</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:170"/>
<font color="Maroon">W1</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>
 ;<br/>


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