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<span class="kw">reconsider </span><font color="Maroon" title="c1">E</font> =  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> 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> ;<br/>
<span class="kw">assume </span><a NAME="E2:52_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_1.html#K2" title="KURATO_1:func.2">Kurat14Set</a> <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:52_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">E</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kurato_1.html#K2" title="KURATO_1:func.2">Kurat14Set</a> <a href="kurato_1.html#K6" title="KURATO_1:func.6">KurExSet</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_1.html#T6" target="_self" title="KURATO_1:th.6">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:52_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D12" title="SETFAM_1:def.12">SETFAM_1:def 12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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