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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">m</font> be  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:216"/>
( <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">W</font> )
 ;<br/>

<a NAME="E2:216"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:216"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:216_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> is <a href="glib_001.html#V3" target="_self">trivial</a>
 ;<br/><a NAME="E2:216_1"/><b>then </b>
1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E44"><i><font color="Green">Lemma147</font></i></a>, </i>;<br/><a NAME="E3:216_1"/><b>then </b>
<font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><b>hence </b><a NAME="E4:216_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:216"/>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/>

<b>hence </b><a NAME="E6:216"/>
<font color="Maroon">W</font> <a href="glib_001.html#K8" target="_self">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> is <a href="glib_001.html#V3" target="_self">trivial</a>
 <b>by </b><i><a class="txt" href="glib_001.html#E44"><i><font color="Green">Lemma147</font></i></a>, </i>;<br/>


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