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<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #), <font color="Maroon">D</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #);<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 ;<br/>

<a NAME="E2:6"/><b>then </b><i><font color="Green">E45</font></i>: 
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">C</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="tops_3.html#T80">TOPS_3:80</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="connsp_1.html#R1">are_separated</a> 
 ;<br/><a NAME="E2:6_1"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <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>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:6_1"/>
<font color="Maroon">C</font>,<font color="Maroon">D</font> <a href="connsp_1.html#R1">are_separated</a> 
 <b>by </b><i>, , <a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:6"/>
<font color="Maroon">C</font>,<font color="Maroon">D</font> <a href="connsp_1.html#R1">are_separated</a> 
 ;<br/>

<a NAME="E5:6"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">D</font> &amp; <font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="connsp_1.html#R1">are_separated</a> 
 <b>by </b><i>, , <a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/>


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