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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="glib_000.html#NM5">inducedSubgraph</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<a NAME="E1:187"/>
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<a NAME="E2:187"/><b>then </b><i><font color="Green">E78</font></i>: 
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D39" target="_self">Def39</a></i>;<br/>
<a NAME="E3:187"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E4:187"/><b>then </b>
(  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="glib_000.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E5:187"/><b>then </b>
(  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp;  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E12"><i><font color="Green">Lemma3</font></i></a></i>;<br/>
<a NAME="E6:187"/><b>then </b>
(  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R1">=</a>  <a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>;<br/>
<b>hence </b><a NAME="E7:187"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5" target="_self">==</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:187"><i><font color="Green">E78</font></i></a>, <a class="txt" href="glib_000.html#E3:187"><i><font color="Green">E79</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self">Def36</a></i>;<br/>


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