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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">W1</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="c4">W2</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>let </b><font color="Maroon" title="c5">m</font>, <font color="Maroon" title="c6">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>









<b>assume </b><a NAME="E1:170"/><i><font color="Green" title="E118">A1</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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" title="c5">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c6">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W1</font> ) or <font color="Maroon" title="c5">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or <font color="Maroon" title="c6">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font> or  not <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">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" title="E119">A2</font></i>: 
( not <font color="Maroon" title="c5">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c6">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W1</font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font> = 
<font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">W2</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:170"><i><font color="Green" title="E118">A1</font></i></a>, <a class="ref" href="glib_001.html#D11" target="_self" title="GLIB_001:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:170"><i><font color="Green" title="E118">A1</font></i></a>, <a class="txt" href="glib_001.html#E1:170_1_1_1"><i><font color="Green" title="E119">A2</font></i></a>, <a class="ref" href="glib_001.html#D11" target="_self" title="GLIB_001:def.11">Def11</a></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" title="E119">A3</font></i>: 
( <font color="Maroon" title="c5">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or <font color="Maroon" title="c6">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">n</font> or  not <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">W1</font> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c3">W1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font> = 
<font color="Maroon" title="c4">W2</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:170"><i><font color="Green" title="E118">A1</font></i></a>, <a class="ref" href="glib_001.html#D11" target="_self" title="GLIB_001:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:170"><i><font color="Green" title="E118">A1</font></i></a>, <a class="txt" href="glib_001.html#E1:170_1_1_2"><i><font color="Green" title="E119">A3</font></i></a>, <a class="ref" href="glib_001.html#D11" target="_self" title="GLIB_001:def.11">Def11</a></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" title="c3">W1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c6">n</font>
 ;<br/>


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