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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/>





<b>assume </b><a NAME="E1:184"/><i><font color="Green">E78</font></i>: 
( <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> &amp; <font color="Maroon">c<sub>3</sub></font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:184"/><b>then </b>
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</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>
 
<b>by </b><i><a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/>
<b>hence </b><a NAME="E3:184"/>
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</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>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self">Def36</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="glib_000.html#D34" target="_self">GLIB_000:def 34</a><br/>

<a NAME="E4:184"/>
 <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</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="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/>
<b>hence </b><a NAME="E5:184"/>
 <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self">Def36</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E6:184"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self">Def36</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="txt" href="glib_000.html#E6:184"><i><font color="Green">E79</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green">E78</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self">Def36</a></i>
;<br/>


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