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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</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><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V1" target="_self">dense</a>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E49</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:72"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_1.html#D3" target="_self">TOPS_1:def 3</a><br/>

<b>thus </b> <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="tops_1.html#E1:72"><i><font color="Green">E48</font></i></a>, <a class="txt" href="tops_1.html#E3:72"><i><font color="Green">E50</font></i></a>, <a class="ref" href="tops_1.html#T81" target="_self">Th81</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="tops_1.html#E2:72"><i><font color="Green">E49</font></i></a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_1.html#D3" target="_self">TOPS_1:def 3</a><br/>


</div>
