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<b>let </b><font color="Maroon">TS</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">GX</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<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/>







<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:40_1"/>
<font color="Maroon">R</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><a NAME="E2:40_1"/><b>then </b>
<font color="Maroon">R</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/><a NAME="E3:40_1"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/><a NAME="E4:40_1"/>
 <a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T30" target="_self">Th30</a></i>;<br/><b>hence </b><a NAME="E5:40_1"/>
 <a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:40"/>
(  <a href="tops_1.html#K1" target="_self">Int</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> implies <font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>


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