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<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> ;<br/>

<b>assume </b><a NAME="E1:82"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#K1">IRRAT</a> 
 ;<br/>

<a NAME="E2:82"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="numbers.html#K3">RAT</a> 
 
<b>by </b><i>, <a class="ref" href="borsuk_5.html#T13">BORSUK_5:13</a></i>;<br/>
<a NAME="E3:82"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K3">R^1</a> 
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T35">BORSUK_5:35</a></i>;<br/>
<a NAME="E4:82"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <a href="topmetr.html#K3">R^1</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T8">TOPS_1:8</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/>


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