<?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><a NAME="E1:10"/><i><font color="Green">E22</font></i>: 
( ( <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> ) or ( <font color="Maroon">K</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">L</font> is <a href="pre_topc.html#V3">open</a> ) )
 ;<br/>

<div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>, <font color="Maroon">L</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/><b>assume </b><a NAME="E1:10_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">K</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">L</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/><a NAME="E2:10_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> &amp; <font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>;<br/><a NAME="E3:10_1"/>
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <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> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> &amp; <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="pre_topc.html#T51">PRE_TOPC:51</a></i>;<br/><a NAME="E4:10_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E5:10_1"/>
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> &amp; <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="pre_topc.html#T51">PRE_TOPC:51</a></i>;<br/><a NAME="E6:10_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E7:10_1"/><i><font color="Green">E31</font></i>: 
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font> )
 <b>by </b><i>, <a class="ref" href="pre_topc.html#T53">PRE_TOPC:53</a></i>;<br/><a NAME="E8:10_1"/>
( <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="subset_1.html#K3">`</a>  &amp; <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font> <a href="subset_1.html#K3">`</a>  )
 ;<br/><a NAME="E9:10_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="pre_topc.html#T53">PRE_TOPC:53</a></i>;<br/><a NAME="E10:10_1"/>
( <font color="Maroon">L</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">L</font> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">K</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">K</font> <a href="subset_1.html#K3">`</a>  )
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E11:10_1"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</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="E12:10_1"/>
( <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> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><a NAME="E13:10_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E14:10_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, , , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E15:10_1"/>
( <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> &amp; <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="subset_1.html#K3">`</a>  )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><a NAME="E16:10_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/><a NAME="E17:10_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E18:10_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">TS</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">TS</font> )
 <b>by </b><i><a class="ref" href="connsp_1.html#D1" target="_self">Def1</a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><a NAME="E19:10_1"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> &amp; <font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><b>hence </b><a NAME="E20:10_1"/>
<font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font>,<font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> <a href="connsp_1.html#R1" target="_self">are_separated</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>, <font color="Maroon">L</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/><b>assume </b><a NAME="E1:10_2"/>
( <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> )
 ;<br/><a NAME="E2:10_2"/><b>then </b><i><font color="Green">E47</font></i>: 
( <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i><a class="ref" href="pre_topc.html#D6">PRE_TOPC:def 6</a></i>;<br/><i><font color="Green">E48</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">K</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>
<br/>.= 
<font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>
;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">TS</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>
<br/>.= 
<font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font>
<b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>
;<br/><b>hence </b><a NAME="E5:10_2"/>
<font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font>,<font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> <a href="connsp_1.html#R1" target="_self">are_separated</a> 
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:10"/>
<font color="Maroon">K</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">L</font>,<font color="Maroon">L</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">K</font> <a href="connsp_1.html#R1" target="_self">are_separated</a> 
 <b>by </b><i>, </i>;<br/>


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