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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">G2</font> be   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font> implies <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font> )</span><br/>





<b>assume </b><a NAME="E1:65"/>
( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font></span><br/>

<a NAME="E2:65"/><b>then </b>
( <font color="Maroon" title="c1">G1</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c3">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c2">G</font> )
 
<b>by </b><i><a class="ref" href="graph_1.html#D25" target="_self" title="GRAPH_1:def.25">Def24</a></i>;<br/>
<a NAME="E3:65"/><b>then </b>
( <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c3">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G</font> )
 
<b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def23</a></i>;<br/>
<a NAME="E4:65"/><b>then </b>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="ref" href="graph_1.html#T22" target="_self" title="GRAPH_1:th.22">Th22</a></i>;<br/>
<a NAME="E5:65"/><b>then </b>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def23</a></i>;<br/>
<b>hence </b><a NAME="E6:65"/>
<font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D25" target="_self" title="GRAPH_1:def.25">Def24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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