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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</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><a NAME="E1:13"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:13"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="tops_1.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a></i>;<br/>


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