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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">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">v</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:160_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 ;<br/><a NAME="E2:160_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font> &amp; ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> or <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> ) )
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="160_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:160_1_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> or <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="160_1_1_1_1"><b>suppose </b></a><a NAME="E1:160_1_1_1_1"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 ;<br/><div class="add"><a NAME="E2:160_1_1_1_1"/><b>then </b>
<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:160_1_1_1_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v</font>,<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D28" target="_self">Def28</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="160_1_1_1_2"><b>suppose </b></a><a NAME="E1:160_1_1_1_2"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font>
 ;<br/><div class="add"><a NAME="E2:160_1_1_1_2"/><b>then </b>
<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:160_1_1_1_2"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v</font>,<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font>,<font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D28" target="_self">Def28</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:160_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v</font>,<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font>,<font color="Maroon">G</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:160"/>
<font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v</font>,<font color="Maroon">v</font> <a href="glib_000.html#K30" target="_self">.adj</a> <font color="Maroon">e</font>,<font color="Maroon">G</font>
 ;<br/>

<b>hence </b><a NAME="E3:160"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 <b>by </b><i/>;<br/>


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