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







<a NAME="E1:217"/><i><font color="Green">E39</font></i>: 
1 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<b>assume </b><a NAME="E2:217"/>
<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">x</font>,<font color="Maroon">G</font>
 ;<br/>

<a NAME="E3:217"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">e</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:217"/>
not <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#V3" target="_self">trivial</a>
 <b>by </b><i><a class="txt" href="glib_001.html#E45"><i><font color="Green">Lemma148</font></i></a>, </i>;<br/>


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