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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>, <font color="Maroon">c<sub>3</sub></font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:191"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R7" target="_self">c&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:191"/><b>then </b><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R6" target="_self">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="glib_000.html#R5" target="_self">==</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D38" target="_self">Def38</a></i>;<br/>
<a NAME="E3:191"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D37" target="_self">Def37</a></i>;<br/>
<a NAME="E4:191"/><b>then </b><i><font color="Green">E81</font></i>: 
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</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="tarski.html#R1">c=</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="191_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:191_1_1"/>
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> )
 </span><b>by </b><i><a class="txt" href="glib_000.html#E2:191"><i><font color="Green">E80</font></i></a>, <a class="ref" href="glib_000.html#T89" target="_self">Th89</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1_1"><b>suppose </b></a><a NAME="E1:191_1_1_1"/>
 <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:191_1_1_1"/>
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E4:191"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="191_1_1_2"><b>suppose </b></a><a NAME="E1:191_1_1_2"/>
 <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:191_1_1_2"/>
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E4:191"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:191"/>
(  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K25" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>3</sub></font> or  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R2">c&lt;</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>


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