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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="E1:53"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="topgen_1.html#V4" target="_self">dense-in-itself</a>
 ;<br/>

<a NAME="E2:53"/><b>then </b><i><font color="Green">E34</font></i>: 
 <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="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K3" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E3:53"/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K3" target="_self">Der</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topgen_1.html#K2" target="_self">Der</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>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T36" target="_self">Th36</a></i>;<br/>
<a NAME="E4:53"/><b>then </b>
 <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="topgen_1.html#K2" target="_self">Der</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>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E2:53"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
 <a href="setfam_1.html#K5">union</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topgen_1.html#V2" target="_self">dense-in-itself</a>
 <b>by </b><i><a class="ref" href="topgen_1.html#D7" target="_self">Def7</a></i>;<br/>


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