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<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:25"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V6">regular_open</a>
 ;<br/>

<a NAME="E2:25"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#D8">TOPS_1:def 8</a></i>;<br/>
<a NAME="E3:25"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T3">TDLAT_3:3</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</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="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T4">TDLAT_3:4</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  is <a href="tops_1.html#V5">regular_closed</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D7">TOPS_1:def 7</a></i>;<br/>


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