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<b>let </b><font color="Maroon">GX</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>



<b>assume </b><a NAME="E1:102"/>
<font color="Maroon">R</font> is <a href="tops_1.html#V5" target="_self">closed_condensed</a>
 ;<br/>

<a NAME="E2:102"/><b>then </b>
<font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tops_1.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E3:102"/><b>then </b>
 <a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
 
;<br/>
<a NAME="E4:102"/><b>then </b>
 <a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E5:102"/>
 <a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i/>;<br/>


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