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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>

<b>set </b><font color="Maroon">EG</font> =  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">SG</font> =  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">TG</font> =  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:61_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</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>
 ;<br/><a NAME="E2:61_1_1"/><b>then </b>
( <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">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font> &amp; <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">x</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><b>hence </b><a NAME="E3:61_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K22" target="_self">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_000.html#E14"><i><font color="Green">Lemma33</font></i></a>, <a class="txt" href="glib_000.html#E12"><i><font color="Green">Lemma31</font></i></a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:61_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="glib_000.html#K22" target="_self">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E3:61_1"/>
<font color="Maroon">x</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>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:61"/>
 <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K22" target="_self">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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