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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><a NAME="E1:80"/>
<font color="Maroon" title="c2">F</font> is <a href="tdlat_2.html#V2" title="TDLAT_2:attr.2">closed-domains-family</a>
 ;<br/>

<a NAME="E2:80"/><b>then </b>
<font color="Maroon" title="c2">F</font> is <a href="tdlat_2.html#V1" title="TDLAT_2:attr.1">domains-family</a>
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T73" target="_self" title="TDLAT_2:th.73">Th73</a></i>;<br/>
<a NAME="E3:80"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T66" target="_self" title="TDLAT_2:th.66">Th66</a></i>;<br/>
<b>hence </b><a NAME="E4:80"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">F</font></span>)</span> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D7" title="TOPS_1:def.7">TOPS_1:def 7</a></i>;<br/>

<b>thus </b><a NAME="E5:80"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a>
 <b>by </b><i><a class="ref" href="tdlat_1.html#T22" title="TDLAT_1:th.22">TDLAT_1:22</a></i>;<br/>


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