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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">G1</font>, <font color="Maroon" title="c3">G2</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:190"/>
<font color="Maroon" title="c2">G1</font> <a href="glib_000.html#R7" title="GLIB_000:pred.7">c&lt;</a> <font color="Maroon" title="c3">G2</font>
 ;<br/>

<a NAME="E2:190"/><b>then </b><i><font color="Green" title="E78">A1</font></i>: 
( <font color="Maroon" title="c2">G1</font> <a href="glib_000.html#R6" title="GLIB_000:pred.6">c=</a> <font color="Maroon" title="c3">G2</font> &amp; not <font color="Maroon" title="c2">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c3">G2</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D38" target="_self" title="GLIB_000:def.38">Def38</a></i>;<br/>
<a NAME="E3:190"/><b>then </b>
<font color="Maroon" title="c2">G1</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c3">G2</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D37" target="_self" title="GLIB_000:def.37">Def37</a></i>;<br/>
<a NAME="E4:190"/><b>then </b><i><font color="Green" title="E79">A2</font></i>: 
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font> &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D34" target="_self" title="GLIB_000:def.34">Def34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="190_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="190_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:190_1_1"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font> or  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> )
 </span><b>by </b><i><a class="txt" href="glib_000.html#E2:190"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="glib_000.html#T89" target="_self" title="GLIB_000:th.89">Th89</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="190_1_1_1"><b>suppose </b></a><a NAME="E1:190_1_1_1"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:190_1_1_1"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font> or  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E4:190"><i><font color="Green" title="E79">A2</font></i></a>, <a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="190_1_1_2"><b>suppose </b></a><a NAME="E1:190_1_1_2"/>
 <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:190_1_1_2"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font> or  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E4:190"><i><font color="Green" title="E79">A2</font></i></a>, <a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">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="E6:190"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c3">G2</font> or  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G1</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> )
 ;<br/>


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