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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="E1:69"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tdlat_2.html#V1" target="_self">domains-family</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/><b>assume </b><a NAME="E2:69_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E3:69_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="tops_1.html#V4">condensed</a>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E1:69"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tdlat_2.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E4:69_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="tops_1.html#D6">TOPS_1:def 6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:69"/>
(  <a href="setfam_1.html#K5">union</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</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> &amp;  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5">union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="setfam_1.html#K5">union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="tdlat_2.html#T57" target="_self">Th57</a></i>;<br/>


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