<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G2</font> be   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#NM3" title="GRAPH_1:NM.3">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="c1">G2</font> iff  <a href="graph_1.html#K9" title="GRAPH_1:func.9">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">G1</font> be   <a href="graph_1.html#V1" title="GRAPH_1:attr.1">strict</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font> iff  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font> )</span><br/>



<span class="kw">thus </span><a NAME="E1:63"/>
( <font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font> implies  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font> implies <font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:63_1"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
<font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font></span><br/>

<a NAME="E2:63_1"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">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#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</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">G1</font> implies <font color="Maroon" title="c3">x</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="c1">G2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_1_1"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c3">x</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">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</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="c1">G2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">G</font> = <font color="Maroon" title="c3">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="c2">G1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="graph_1.html#D25" target="_self" title="GRAPH_1:def.25">Def25</a></span>;<br/>
<a NAME="E3:63_1_1"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c2">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></span>;<br/>
<a NAME="E4:63_1_1"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E3:63_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="graph_1.html#T17" target="_self" title="GRAPH_1:th.17">Th17</a></span>;<br/>
<a NAME="E5:63_1_1"/><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<font color="Maroon" title="c4">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="c1">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63_1_1"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:63_1_1"/>
<font color="Maroon" title="c3">x</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="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_1_1"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="ref" href="graph_1.html#D25" target="_self" title="GRAPH_1:def.25">Def25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E3:63_1"/>
 <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:63"/><span class="lab"><font color="Green" title="E31">A7</font></span>: 
 <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c2">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_1.html#K9" title="GRAPH_1:func.9">bool</a> <font color="Maroon" title="c1">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font></span><br/>

<a NAME="E3:63"/><span class="lab"><font color="Green" title="E32">A8</font></span>: 
<font color="Maroon" title="c2">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">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="graph_1.html#T31" target="_self" title="GRAPH_1:th.31">Th31</a></span>;<br/>
<a NAME="E4:63"/><span class="lab"><font color="Green" title="E33">A9</font></span>: 
<font color="Maroon" title="c2">G1</font> is    <a href="graph_1.html#M3" title="GRAPH_1:mode.3">Subgraph</a> of <font color="Maroon" title="c1">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E31">A7</font></span></a>, <a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="ref" href="graph_1.html#D25" target="_self" title="GRAPH_1:def.25">Def25</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:63"/>
<font color="Maroon" title="c2">G1</font> <a href="graph_1.html#R4" title="GRAPH_1:pred.4">c=</a> <font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="ref" href="graph_1.html#D24" target="_self" title="GRAPH_1:def.24">Def24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
