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<b>let </b><font color="Maroon" title="c1">FT</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st <font color="Olive" title="b1">A</font> is <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a> holds <br/><font color="Olive" title="b1">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">closed</a></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a> implies <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">closed</a> )</span><br/>



<b>assume </b><a NAME="E1:42"/>
<font color="Maroon" title="c2">A</font> is <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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">closed</a></span><br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <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" target="_self" title="FIN_TOPO:def.16">Def16</a></i>;<br/>
<a NAME="E3:42"/>
<font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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#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" target="_self" title="FIN_TOPO:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:42"/>
<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">closed</a>
 <b>by </b><i><a class="txt" href="fin_topo.html#E2:42"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="fin_topo.html#D17" target="_self" title="FIN_TOPO:def.17">Def17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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