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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>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>, <font color="Maroon">A1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FT</font>, <font color="Maroon">B1</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="E1:40"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="fintopo4.html#R1">are_separated</a> 
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E3:40"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E4:40"/>
( <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> &amp; <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>, <a class="ref" href="fintopo4.html#D1">FINTOPO4:def 1</a></i>;<br/>
<a NAME="E5:40"/><b>then </b><i><font color="Green">E41</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:40"/>
( <font color="Maroon">A1</font> <a href="fin_topo.html#K9">^b</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a>  &amp; <font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a>  <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#T19">FIN_TOPO:19</a></i>;<br/>
<a NAME="E7:40"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> &amp; <font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<a NAME="E8:40"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font> &amp; <font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">FT</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E9:40"/><b>then </b>
( <font color="Maroon">A1</font> <a href="fin_topo.html#K9">^b</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">A1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B1</font> <a href="fin_topo.html#K9">^b</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E10:40"/>
<font color="Maroon">A1</font>,<font color="Maroon">B1</font> <a href="fintopo4.html#R1">are_separated</a> 
 <b>by </b><i><a class="ref" href="fintopo4.html#D1">FINTOPO4:def 1</a></i>;<br/>


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