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<b>let </b><font color="Maroon">FT</font> be  non <a href="struct_0.html#V3">empty</a> <a href="fin_topo.html#V1">filled</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>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">FT</font> is <a href="fin_topo.html#V2">symmetric</a>
 ;<br/>

<b>thus </b><a NAME="E2:9"/>
( <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1" target="_self">are_separated</a>  implies <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> )
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E3:9"/>
( <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> implies <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1" target="_self">are_separated</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1"/><i><font color="Green">E27</font></i>: 
<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="E2:9_1"/><b>then </b>
<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> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:9_1"/>
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1" target="_self">are_separated</a> 
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>


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