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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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/>

<b>assume </b><b>that </b><br/><a NAME="E1:105_1_2"/><i><font color="Green">E52</font></i>: 
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> holds <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:105_1_2"/><i><font color="Green">E53</font></i>: 
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> holds <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E3:105_1_2"/><i><font color="Green">E54</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>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E1:105_1_2"><i><font color="Green">E52</font></i></a></i>;<br/>
<a NAME="E4:105_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E2:105_1_2"><i><font color="Green">E53</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:105_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3:105_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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