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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W1</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:245"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a> </span>)</span> <a href="glib_000.html#K29">.edgesInOut()</a>  )
 ;<br/>

<a NAME="E2:245"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R1">Joins</a> <font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a> ,<span class="p1">(<span class="default"><font color="Maroon">W2</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">G2</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T70">GLIB_000:70</a></i>;<br/>
<b>set </b><font color="Maroon">W1B</font> = <font color="Maroon">G1</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">W1</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">W1</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>set </b><font color="Maroon">W2B</font> = <font color="Maroon">G2</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">W2</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">W2</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/>
<a NAME="E3:245"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">W1</font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:245"/>
<span class="p1">(<span class="default"><font color="Maroon">W1</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> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">W2</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>
 
<b>by </b><i>, <a class="ref" href="glib_000.html#T83">GLIB_000:83</a></i>;<br/>
<a NAME="E5:245"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">G1</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">W1</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">W1</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> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font> <a href="glib_001.html#K2" target="_self">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon">W2</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">W2</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>
 
<b>by </b><i><a class="txt" href="glib_001.html#E56"><i><font color="Green">Lemma160</font></i></a>, <a class="txt" href="glib_001.html#E57"><i><font color="Green">Lemma161</font></i></a>, <a class="txt" href="glib_001.html#E55"><i><font color="Green">Lemma158</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:245"/>
<font color="Maroon">W1</font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> <a href="glib_001.html#K10" target="_self">.addEdge</a> <font color="Maroon">e</font>
 <b>by </b><i>, , </i>;<br/>


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