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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#NM2">_Graph</a>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:139_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">G1</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G2</font> &amp; <font color="Maroon">G2</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font> )
 ;<br/><a NAME="E2:139_1"/><b>then </b>
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> &amp; ( for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> holds <br/>( <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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> ) ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:139_1"/>
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/><a NAME="E4:139_1"/><b>then </b><i><font color="Green">E29</font></i>: 
(  <a href="relset_1.html#K4">dom</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="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> &amp;  <a href="relset_1.html#K4">dom</a> <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="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> &amp;  <a href="relset_1.html#K4">dom</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="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> &amp;  <a href="relset_1.html#K4">dom</a> <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="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> )
 <b>by </b><i/>;<br/><a NAME="E5:139_1"/>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</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> holds <br/><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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:139_1"/>
 <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E7:139_1"/>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</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> holds <br/><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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E8:139_1"/>
 <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:139"/><i><font color="Green">E30</font></i>: 
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">G2</font> &amp;  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">G2</font> )
 ;<br/>

<a NAME="E3:139"/><b>then </b>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G1</font> holds <br/>( <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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</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="Olive">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">G2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> )
 
;<br/>
<b>hence </b><a NAME="E4:139"/>
( <font color="Maroon">G1</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G2</font> &amp; <font color="Maroon">G2</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font> )
 <b>by </b><i>, </i>;<br/>


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