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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">e</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">v</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:102"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> ,<font color="Maroon">v</font>,<font color="Maroon">G</font> &amp; <font color="Maroon">W</font> is <a href="glib_001.html#V5" target="_self">Path-like</a> &amp; not <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="glib_001.html#K13" target="_self">.vertices()</a>  &amp; ( <font color="Maroon">W</font> is <a href="glib_001.html#V3" target="_self">trivial</a> or  not <font color="Maroon">W</font> is <a href="glib_001.html#V1" target="_self">closed</a> ) )
 ;<br/>

<a NAME="E2:102"/><i><font color="Green">E40</font></i>: 
not <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> <a href="glib_001.html#K14" target="_self">.edges()</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:102"/>
for <font color="Olive">n</font> being <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> holds <br/><font color="Maroon">v</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="Olive">n</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:102"/>
<font color="Maroon">W</font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">e</font> is <a href="glib_001.html#V5" target="_self">Path-like</a>
 <b>by </b><i>, , </i>;<br/>


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