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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>, <font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:102"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">G1</font> <a href="glib_000.html#R5">==</a> <font color="Maroon">G2</font>
 ;<br/>

<b>let </b><font color="Maroon">W1</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">G2</font>;<br/>



<b>assume </b><a NAME="E2:102"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font>
 ;<br/>

<b>given </b><font color="Maroon">m</font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">n</font> being  <a href="abian.html#V1">odd</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E3:102"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> 2 <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">W1</font> &amp; <font color="Maroon">W1</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">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>and </b><br/><a NAME="E4:102"/><i><font color="Green">E56</font></i>: 
 ex <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G1</font>
 <b>and </b><br/><a NAME="E5:102"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">f</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W1</font> <a href="glib_001.html#K14">.edges()</a>  holds <br/> not <font color="Olive">f</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="chord.html#D10" target="_self">CHORD:def 10</a><br/>

<b>take </b>
<font color="Maroon">m</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="chord.html#D10" target="_self">CHORD:def 10</a><br/>

<b>take </b>
<font color="Maroon">n</font>
;<br/>

<b>thus </b><a NAME="E6:102"/>
( <font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> 2 <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">W2</font> &amp; <font color="Maroon">W2</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">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i>, </i>;<br/>

<b>consider </b><font color="Maroon">e</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:102"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G1</font>
 <b>by </b><i><a class="ref" href="chord.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E9:102"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G2</font>
 
<b>by </b><i>, , , <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/>
<b>hence </b><a NAME="E10:102"/>
 ex <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G2</font>
 ;<br/>

<b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E11:102"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W2</font> <a href="glib_001.html#K14">.edges()</a> 
 ;<br/>

<a NAME="E12:102"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W1</font> <a href="glib_001.html#K14">.edges()</a> 
 
<b>by </b><i>, <a class="ref" href="glib_001.html#T111">GLIB_001:111</a></i>;<br/>
<a NAME="E13:102"/><b>then </b>
not <font color="Maroon">f</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G1</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E14:102"/>
not <font color="Maroon">f</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>,<font color="Maroon">W2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>,<font color="Maroon">G2</font>
 <b>by </b><i>, , <a class="ref" href="glib_000.html#T91">GLIB_000:91</a></i>;<br/>


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