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

<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:42_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E3:42_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies ( <font color="Maroon">x</font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>] ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:42_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:42_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:42_1_1"/>
<font color="Maroon">x</font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E4:42_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>]
 <b>by </b><i>, </i>;<br/>


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

<b>assume </b><a NAME="E4:42_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">x</font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>] )
 ;<br/>

<a NAME="E5:42_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="graph_1.html#K7" target="_self">bool</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:42_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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