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<b>let </b><font color="Maroon">c<sub>1</sub></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">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="E1:27"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<a NAME="E3:27"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="yellow_8.html#E1:27"><i><font color="Green">E20</font></i></a>, <a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/>
<a NAME="E4:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finsub_1.html#K2">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></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/>
<b>hence </b><a NAME="E5:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="finsub_1.html#K2">\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="yellow_8.html#E2:27"><i><font color="Green">E21</font></i></a>, <a class="txt" href="yellow_8.html#E3:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="tops_1.html#T35">TOPS_1:35</a></i>;<br/>


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