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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/>







<b>set </b><font color="Maroon">W2</font> = <font color="Maroon">W</font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">e</font>;<br/>
<b>set </b><font color="Maroon">WB</font> = <font color="Maroon">G</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">e</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">e</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:206"/>
<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="E2:206"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K29">.edgesInOut()</a> 
 
<b>by </b><i><a class="ref" href="glib_000.html#T65">GLIB_000:65</a></i>;<br/>
<a NAME="E3:206"/><b>then </b><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> ,<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">e</font>,<font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T70">GLIB_000:70</a></i>;<br/>
<a NAME="E4:206"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">e</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="glib_001.html#K14" target="_self">.edges()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">e</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="txt" href="glib_001.html#E41"><i><font color="Green">Lemma143</font></i></a></i>;<br/>
<a NAME="E5:206"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span>,<font color="Maroon">e</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K30">.adj</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:206"/>
<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="glib_001.html#K14" target="_self">.edges()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K14" target="_self">.edges()</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">e</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_001.html#E42"><i><font color="Green">Lemma145</font></i></a>, <a class="ref" href="glib_001.html#D30" target="_self">Def30</a></i>;<br/>


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