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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_1_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">IT</font> is <a href="prob_1.html#V1">compl-closed</a>
 ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:11_1_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 ;<br/><b>then reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> ;<br/><a NAME="E4:11_1_1_1"/>
<font color="Maroon">A'</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 <b>by </b><i>, , <a class="ref" href="prob_1.html#D1">PROB_1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:11_1_1_1"/>
<font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:11_1_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> holds <br/><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="prob_1.html#D1">PROB_1:def 1</a><br/>

<b>assume </b><a NAME="E3:11_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 ;<br/>

<a NAME="E4:11_1_1"/><b>then </b>
<font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:11_1_1"/>
<font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 ;<br/>


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