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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:88"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tdlat_2.html#V3" target="_self">open-domains-family</a>
 ;<br/>

<a NAME="E2:88"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is <a href="tdlat_2.html#V1" target="_self">domains-family</a>
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T80" target="_self">Th80</a></i>;<br/>
<a NAME="E3:88"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T67" target="_self">Th67</a></i>;<br/>
<b>hence </b><a NAME="E4:88"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="tops_1.html#V6">open_condensed</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D8">TOPS_1:def 8</a></i>;<br/>

<b>thus </b><a NAME="E5:88"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5">union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="tops_1.html#V6">open_condensed</a>
 <b>by </b><i><a class="ref" href="tdlat_1.html#T23">TDLAT_1:23</a></i>;<br/>


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