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<span class="kw">let </span><font color="Maroon" title="c1">FMT</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fintopo2.html#L1" title="FINTOPO2:struct.1">FMT_Space_Str</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">FMT</font>  st <font color="Olive" title="b1">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fintopo2.html#V3" title="FINTOPO2:attr.3">Fo_open</a>  holds <br/><font color="Olive" title="b1">A</font> is  <a href="fintopo2.html#V4" title="FINTOPO2:attr.4">Fo_closed</a> </span><br/><span class="kw">let </span><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">FMT</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="fintopo2.html#V3" title="FINTOPO2:attr.3">Fo_open</a>  implies <font color="Maroon" title="c2">A</font> is  <a href="fintopo2.html#V4" title="FINTOPO2:attr.4">Fo_closed</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:57"/>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fintopo2.html#V3" title="FINTOPO2:attr.3">Fo_open</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is  <a href="fintopo2.html#V4" title="FINTOPO2:attr.4">Fo_closed</a> </span><br/>

<a NAME="E2:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<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="fintopo2.html#K10" title="FINTOPO2:func.10">^Foi</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo2.html#D16" target="_self" title="FINTOPO2:def.16">Def16</a></span>;<br/>
<a NAME="E3:57"/>
<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="fintopo2.html#K10" title="FINTOPO2:func.10">^Foi</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>  <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="fintopo2.html#K9" title="FINTOPO2:func.9">^Fob</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo2.html#T39" target="_self" title="FINTOPO2:th.39">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:57"/>
<font color="Maroon" title="c2">A</font> is  <a href="fintopo2.html#V4" title="FINTOPO2:attr.4">Fo_closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="fintopo2.html#D17" target="_self" title="FINTOPO2:def.17">Def17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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