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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <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>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a>
 <b>and </b><br/><a NAME="E3:9"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">C</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Olive">C</font> &amp; <font color="Olive">C</font> is <a href="pre_topc.html#V4">closed</a> holds <br/><font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">C</font>
 ;<br/>

<a NAME="E4:9"/>
( <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E6:9"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i>, , <a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>


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