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

<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">FX</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">FX</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">CFX</font> =  <a href="pcomps_1.html#K2" target="_self">clf</a> <font color="Maroon">FX</font> as    <a href="hidden.html#M1">set</a>  ;<br/>
<b>assume </b><a NAME="E3:13"/><i><font color="Green">E27</font></i>: 
not  <a href="pcomps_1.html#K2" target="_self">clf</a> <font color="Maroon">FX</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E4:13"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   holds not <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">CFX</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:13_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">CFX</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E3:13_1"/>
 ex <font color="Olive">V</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">V</font> &amp; <font color="Olive">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FX</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:13_1"/>
contradiction
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">X</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">CFX</font>;<br/>
<a NAME="E6:13"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">CFX</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:13"/>
contradiction
 <b>by </b><i/>;<br/>


</div>
