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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>





<b>assume </b><a NAME="E1:184"/><i><font color="Green" title="E78">A1</font></i>: 
( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">G3</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font> )
 ;<br/>

<a NAME="E2:184"/><b>then </b>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>;<br/>
<b>hence </b><a NAME="E3:184"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self" title="GLIB_000:def.36">Def36</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">GLIB_000:def 34</a><br/>

<a NAME="E4:184"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>;<br/>
<b>hence </b><a NAME="E5:184"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self" title="GLIB_000:def.36">Def36</a></i>;<br/>

<b>let </b><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E6:184"/><i><font color="Green" title="E79">A2</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G3</font>
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self" title="GLIB_000:def.36">Def36</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="txt" href="glib_000.html#E6:184"><i><font color="Green" title="E79">A2</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>
<b>by </b><i><a class="txt" href="glib_000.html#E1:184"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" target="_self" title="GLIB_000:def.36">Def36</a></i>
;<br/>


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