<?xml version="1.0"?>
<div class="add">

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="topgen_4.html#T18" target="_self">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="prob_1.html#V1">compl-closed</a> <a href="topgen_4.html#V1" target="_self">all-open-containing</a> <a href="topgen_4.html#V3" target="_self">closed_for_countable_unions</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:105_1_1"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="prob_1.html#V1">compl-closed</a> <a href="topgen_4.html#V1" target="_self">all-open-containing</a> <a href="topgen_4.html#V3" target="_self">closed_for_countable_unions</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="topgen_4.html#T67" target="_self">Th67</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="prob_1.html#V1">compl-closed</a> <a href="topgen_4.html#V1" target="_self">all-open-containing</a> <a href="topgen_4.html#V3" target="_self">closed_for_countable_unions</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E4:105_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E5:105_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3:105_1_1"><i><font color="Green">E52</font></i></a></i>;<br/>


</div>
