<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">TS</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green">E22</font></i>: 
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">L</font> &amp; <font color="Maroon">K</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">L</font> is <a href="pre_topc.html#V4">closed</a> )
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">K</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E3:3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">L</font> <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="E4:3"/>
( <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">K</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">L</font> &amp; <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">L</font> )
 
<b>by </b><i>, <a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<a NAME="E5:3"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">K</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">L</font> &amp; <font color="Maroon">K</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:3"/>
<font color="Maroon">K</font>,<font color="Maroon">L</font> <a href="connsp_1.html#R1" target="_self">are_separated</a> 
 <b>by </b><i/>;<br/>


</div>
