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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" target="_self">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>thus </b><a NAME="E1:165"/>
( <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font> implies <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font> )
 <b>by </b><i/>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:165_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font>
 ;<br/><a NAME="E2:165_1"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/><a NAME="E3:165_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:165_1"/>
<font color="Maroon">e</font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:165_2"/>
<font color="Maroon">e</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font>
 ;<br/><a NAME="E2:165_2"/><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#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp; ( ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> ) or ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> ) ) )
 <b>by </b><i/>;<br/><a NAME="E3:165_2"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</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">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</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">G1</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="E4:165_2"/>
<font color="Maroon">e</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:165"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font>
 ;<br/>

<a NAME="E5:165"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:165"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</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">G1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font></span>)</span> <a href="funct_1.html#K1">.</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">G1</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="E7:165"/>
<font color="Maroon">e</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font>
 <b>by </b><i>, </i>;<br/>


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