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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fin_topo.html#L1">FT_Space_Str</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="fin_topo.html#V5">closed</a>
 ;<br/>

<a NAME="E2:5"/><b>then </b><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="fin_topo.html#K8">^b</a> 
 
<b>by </b><i><a class="ref" href="fin_topo.html#D16">FIN_TOPO:def 16</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="fin_topo.html#K8">^b</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="fin_topo.html#K7">^i</a> </span>)</span> <a href="subset_1.html#K3">`</a> 
<b>by </b><i><a class="ref" href="fin_topo.html#T22">FIN_TOPO:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K7">^i</a> </span>)</span> <a href="subset_1.html#K3">`</a> 

;<br/>
<b>then </b><font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K7">^i</a> </span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> 
<b>by </b><i><a class="txt" href="fintopo2.html#E2:5"><i><font color="Green">E2</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K7">^i</a> 

;<br/>
<b>hence </b><a NAME="E5:5"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="fin_topo.html#V4">open</a>
 <b>by </b><i><a class="ref" href="fin_topo.html#D15">FIN_TOPO:def 15</a></i>;<br/>


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