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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x0</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">T</font> =  <a href="topgen_2.html#K5" target="_self">DiscrWithInfin</a> <font color="Maroon">X</font>,<font color="Maroon">x0</font>;<br/>
<a NAME="E1:38"/><i><font color="Green">E29</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" target="_self">DiscrWithInfin</a> <font color="Maroon">X</font>,<font color="Maroon">x0</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" target="_self">DiscrWithInfin</a> <font color="Maroon">X</font>,<font color="Maroon">x0</font></span>)</span>;<br/>

<a NAME="E2:38"/>
( <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> iff <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T29">TOPS_1:29</a></i>;<br/>
<a NAME="E3:38"/><b>then </b>
( <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> iff (  not <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  or <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="finset_1.html#V1">finite</a> ) )
 
<b>by </b><i><a class="ref" href="topgen_2.html#T1" target="_self">Th1</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
( <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> iff not <!--HUMANRECFAILED-->( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; not <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">A</font> is <a href="finset_1.html#V1">finite</a> ) )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


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