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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <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/>



<a NAME="E1:15"/>
 <a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font> is <a href="tops_2.html#V2">closed</a>
 
<b>by </b><i><a class="ref" href="pcomps_1.html#T14">PCOMPS_1:14</a></i>;<br/>
<a NAME="E2:15"/><b>then </b>
(  <a href="setfam_1.html#K6">meet</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="pre_topc.html#V4">closed</a> &amp;  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K6">meet</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T13" target="_self">Th13</a>, <a class="ref" href="tops_2.html#T29">TOPS_2:29</a></i>;<br/>
<a NAME="E3:15"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6">meet</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K6">meet</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="pre_topc.html#K4">Cl</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> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6">meet</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a>, <a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<b>hence </b><a NAME="E4:15"/>
 <a href="pre_topc.html#K4">Cl</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> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K6">meet</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" target="_self">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


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