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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">x1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>











<b>assume </b><a NAME="E1:117"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">G</font> &amp; <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">G</font> )
 ;<br/>

<b>set </b><font color="Maroon">S</font> = <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>;<br/>
<b>set </b><font color="Maroon">T</font> = <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>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:117_1_1"/>
( ( <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">x1</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> ) or ( <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">y1</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> ) )
 </span><b>by </b><i><a class="ref" href="glib_000.html#D19" target="_self">Def19</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_1"><b>suppose </b></a><a NAME="E1:117_1_1_1"/><i><font color="Green">E29</font></i>: 
( <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">x1</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:117_1_1_1_1_1"/>
( ( <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">x2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <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">y2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 </span><b>by </b><i><a class="ref" href="glib_000.html#D19" target="_self">Def19</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:117_1_1_1_1_1_1"/>
( <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">x2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:117_1_1_1_1_1_1"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:117_1_1_1_1_1_2"/>
( <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">y2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:117_1_1_1_1_1_2"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:117_1_1_1"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_2"><b>suppose </b></a><a NAME="E1:117_1_1_2"/><i><font color="Green">E30</font></i>: 
( <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">y1</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> )
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:117_1_1_2_1_1"/>
( ( <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">x2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <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">y2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 </span><b>by </b><i><a class="ref" href="glib_000.html#D19" target="_self">Def19</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:117_1_1_2_1_1_1"/>
( <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">x2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:117_1_1_2_1_1_1"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="117_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:117_1_1_2_1_1_2"/>
( <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">y2</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">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:117_1_1_2_1_1_2"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:117_1_1_2"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:117"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) )
 ;<br/>


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