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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">x0</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">T</font> =  <a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font>;<br/>
<a NAME="E1:38"/><i><font color="Green" title="E25">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="topgen_2.html#D5" target="_self" title="TOPGEN_2:def.5">Def5</a></i>;<br/>
<b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font></span>)</span>;<br/>

<a NAME="E2:38"/>
( <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> iff <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T29" title="TOPS_1:th.29">TOPS_1:29</a></i>;<br/>
<a NAME="E3:38"/><b>then </b>
( <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> iff (  not <font color="Maroon" title="c2">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  or <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> ) )
 
<b>by </b><i><a class="ref" href="topgen_2.html#T21" target="_self" title="TOPGEN_2:th.21">Th21</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
( <font color="Maroon" title="c4">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> iff not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; not <font color="Maroon" title="c2">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> &amp; not <font color="Maroon" title="c4">A</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> ) )
 <b>by </b><i><a class="txt" href="topgen_2.html#E1:38"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>


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