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<b>let </b><font color="Maroon" title="c3">G2</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G1</font> being <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a> <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a> holds <br/> ( <font color="Olive" title="b1">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font> iff  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Olive" title="b1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font> )</span><br/><b>let </b><font color="Maroon" title="c4">G1</font> be  <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a> <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">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="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font> iff  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font> )</span><br/>



<b>thus </b><a NAME="E1:66"/>
( <font color="Maroon" title="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font> implies  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font> implies <font color="Maroon" title="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:66_1"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font></span><br/>

<a NAME="E2:66_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font> )</span><br/>

<b>assume </b><a NAME="E1:66_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">G</font> = <font color="Maroon" title="c5">x</font> as  <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a>  <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c4">G1</font> <b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></i>;<br/>
<a NAME="E3:66_1_1"/>
<font color="Maroon" title="c6">G</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c4">G1</font>
 
<b>by </b><i><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def23</a></i>;<br/>
<a NAME="E4:66_1_1"/><b>then </b>
<font color="Maroon" title="c6">G</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font>
 
<b>by </b><i><a class="txt" href="graph_1.html#E1:66_1"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="graph_1.html#T17" target="_self" title="GRAPH_1:th.17">Th17</a></i>;<br/>
<a NAME="E5:66_1_1"/><b>then </b>
<font color="Maroon" title="c6">G</font> is  <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a>  <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c3">G2</font>
 
<b>by </b><i><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def23</a></i>;<br/>
<b>hence </b><a NAME="E6:66_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">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/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:66_1"/>
 <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:66"/><i><font color="Green" title="E39">A2</font></i>: 
 <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c3">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font></span><br/>

<a NAME="E3:66"/>
<font color="Maroon" title="c4">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_1.html#K7" title="GRAPH_1:func.7">bool</a> <font color="Maroon" title="c4">G1</font>
 
<b>by </b><i><a class="ref" href="graph_1.html#T31" target="_self" title="GRAPH_1:th.31">Th31</a></i>;<br/>
<a NAME="E4:66"/><b>then </b>
<font color="Maroon" title="c4">G1</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c3">G2</font>
 
<b>by </b><i><a class="txt" href="graph_1.html#E2:66"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
<font color="Maroon" title="c4">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c3">G2</font>
 <b>by </b><i><a class="ref" href="graph_1.html#D23" target="_self" title="GRAPH_1:def.23">Def23</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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