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

<b>set </b><font color="Maroon" title="c1">A</font> =  <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a> ;<br/>
<b>assume </b><a NAME="E1:63"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a> ,<span class="p2">(<span class="default"><a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>  <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="kurato_1.html#K3" title="KURATO_1:func.3">Kurat14ClPart</a> <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:63"/><i><font color="Green" title="E49">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a> ,<span class="p2">(<span class="default"><a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>  <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_1.html#K3" title="KURATO_1:func.3">Kurat14ClPart</a> <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <b>by </b><i><a class="txt" href="kurato_1.html#E3:63"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>
<a NAME="E5:63"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c3">x</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:63"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="tops_2.html#D2" title="TOPS_2:def.2">TOPS_2:def 2</a></i>;<br/>
<a NAME="E6:63"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>  <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:63"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E7:63"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a> 
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:63"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="tops_2.html#D2" title="TOPS_2:def.2">TOPS_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:63"/>
contradiction
 <b>by </b><i><a class="txt" href="kurato_1.html#E5:63"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="tops_1.html#T29" title="TOPS_1:th.29">TOPS_1:29</a></i>;<br/>


</div>
