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<b>let </b><font color="Maroon" title="c1">FT</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>;<br/>



<b>assume </b><a NAME="E1:4"/>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">open</a>
 ;<br/>

<a NAME="E2:4"/><b>then </b><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a> 
 
<b>by </b><i><a class="ref" href="fin_topo.html#D16" title="FIN_TOPO:def.16">FIN_TOPO:def 16</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="ref" href="fin_topo.html#T23" title="FIN_TOPO:th.23">FIN_TOPO:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 

;<br/>
<b>then </b><font color="Maroon" title="c2">A</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="txt" href="fintopo2.html#E2:4"><i><font color="Green" title="E2">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 

;<br/>
<b>hence </b><a NAME="E5:4"/>
<font color="Maroon" title="c2">A</font> is <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">closed</a>
 <b>by </b><i><a class="ref" href="fin_topo.html#D17" title="FIN_TOPO:def.17">FIN_TOPO:def 17</a></i>;<br/>


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