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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="kurato_1.html#K6" target="_self">KurExSet</a> ;<br/>
<b>assume </b><a NAME="E1:66"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="kurato_1.html#K6" target="_self">KurExSet</a> ,<span class="p2">(<span class="default"><a href="kurato_1.html#K6" target="_self">KurExSet</a>  <a href="subset_1.html#K3">`</a> </span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="kurato_1.html#K4" target="_self">Kurat14OpPart</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:66"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><a href="kurato_1.html#K6" target="_self">KurExSet</a> ,<span class="p2">(<span class="default"><a href="kurato_1.html#K6" target="_self">KurExSet</a>  <a href="subset_1.html#K3">`</a> </span>)</span></span><a href="tarski.html#K2">}</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K4" target="_self">Kurat14OpPart</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="txt" href="kurato_1.html#E3:66"><i><font color="Green">E51</font></i></a></i>;<br/>
<a NAME="E5:66"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:66"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a></i>;<br/>
<a NAME="E6:66"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="kurato_1.html#K6" target="_self">KurExSet</a>  or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a>  <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:66"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E7:66"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 
<b>by </b><i><a class="txt" href="kurato_1.html#E3:66"><i><font color="Green">E51</font></i></a>, <a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:66"/>
contradiction
 <b>by </b><i><a class="txt" href="kurato_1.html#E5:66"><i><font color="Green">E52</font></i></a>, <a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/>


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