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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#NM5">Path</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:225"/><i><font color="Green">E39</font></i>: 
not <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a>
 ;<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="E2:225"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&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/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="225_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:225_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:225_1"/><b>then </b>
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E48"><i><font color="Green">Lemma151</font></i></a>, </i>;<br/><b>hence </b><a NAME="E3:225_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_001.html#E47"><i><font color="Green">Lemma150</font></i></a>, <a class="txt" href="glib_001.html#E49"><i><font color="Green">Lemma152</font></i></a>, <a class="txt" href="glib_001.html#E42"><i><font color="Green">Lemma145</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:225"/>
<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>


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