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<b>let </b><font color="Maroon">TS</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/>





<a NAME="E1:18"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Q</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<b>assume </b><a NAME="E2:18"/>
( <font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">Q</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>

<a NAME="E3:18"/><b>then </b>
( <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">Q</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:18"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font></span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:18"/>
<font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i/>;<br/>


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