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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">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:4"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="lopclset.html#K1" target="_self">OpenClosedSet</a> <font color="Maroon">T</font>
 ;<br/>

<a NAME="E2:4"/><b>then </b>
 ex <font color="Olive">Z</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">Z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp; <font color="Olive">Z</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">Z</font> is <a href="pre_topc.html#V4">closed</a> )
 
;<br/>
<b>hence </b><a NAME="E3:4"/>
<font color="Maroon">X</font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>


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