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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fin_topo.html#L1">FT_Space_Str</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:8"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="fin_topo.html#V3">symmetric</a>
 ;<br/>

<a NAME="E2:8"/><b>then </b><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K8">^b</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K11">^f</a> 
 
<b>by </b><i><a class="ref" href="fin_topo.html#T17">FIN_TOPO:17</a></i>;<br/>
<a NAME="E3:8"/>
<font color="Maroon">c<sub>3</sub></font> <a href="fin_topo.html#K8">^b</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="fin_topo.html#K11">^f</a> 
 
<b>by </b><i><a class="txt" href="fintopo4.html#E1:8"><i><font color="Green">E4</font></i></a>, <a class="ref" href="fin_topo.html#T17">FIN_TOPO:17</a></i>;<br/>
<b>hence </b><a NAME="E4:8"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="fintopo4.html#R1" target="_self">are_separated</a>  iff ( <font color="Maroon">c<sub>2</sub></font> <a href="fin_topo.html#K11">^f</a>  <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font> <a href="fin_topo.html#K11">^f</a>  ) )
 <b>by </b><i><a class="txt" href="fintopo4.html#E2:8"><i><font color="Green">E5</font></i></a>, <a class="ref" href="fintopo4.html#D1" target="_self">Def1</a></i>;<br/>


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