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<b>let </b><font color="Maroon">FT</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">FT</font> is <a href="fin_topo.html#V1">filled</a> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">FT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> )
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1">are_separated</a> 
 ;<br/>

<a NAME="E3:39"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 
<b>by </b><i>, <a class="ref" href="fintopo4.html#T6">FINTOPO4:6</a>, </i>;<br/>
<a NAME="E4:39"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a>  &amp; <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a>  )
 
<b>by </b><i><a class="ref" href="fin_topo.html#T18">FIN_TOPO:18</a>, </i>;<br/>
<div><i><font color="Green">E43</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_1"/>
<font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:39_1"/><b>then </b>
<font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T73">XBOOLE_1:73</a></i>;<br/><b>hence </b><a NAME="E3:39_1"/>
<font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_2"/>
<font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a> 
 ;<br/><a NAME="E2:39_2"/><b>then </b>
<font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T73">XBOOLE_1:73</a></i>;<br/><b>hence </b><a NAME="E3:39_2"/>
<font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:39"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">A</font> is <a href="fin_topo.html#V4">closed</a> &amp; <font color="Maroon">B</font> is <a href="fin_topo.html#V4">closed</a> )
 
<b>by </b><i><a class="ref" href="fin_topo.html#D17">FIN_TOPO:def 17</a>, , , , <a class="ref" href="fintopo4.html#D1">FINTOPO4:def 1</a></i>;<br/>
<a NAME="E8:39"/>
<font color="Maroon">B</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="pre_topc.html#T25">PRE_TOPC:25</a></i>;<br/>
<b>hence </b><a NAME="E9:39"/>
( <font color="Maroon">A</font> is <a href="fin_topo.html#V3">open</a> &amp; <font color="Maroon">A</font> is <a href="fin_topo.html#V4">closed</a> )
 <b>by </b><i>, <a class="ref" href="fin_topo.html#T31">FIN_TOPO:31</a></i>;<br/>


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