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<b>let </b><font color="Maroon" title="c2">R1</font>, <font color="Maroon" title="c3">R2</font> be  <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a> <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a> <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:104_1_2"/><i><font color="Green" title="E51">A2</font></i>: 
for <font color="Olive" title="b1">G</font> being <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a> <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a> <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c2">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">G</font>
 <b>and </b><br/><a NAME="E2:104_1_2"/><i><font color="Green" title="E52">A3</font></i>: 
for <font color="Olive" title="b1">G</font> being <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a> <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a> <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">G</font>
 ;<br/>

<a NAME="E3:104_1_2"/><i><font color="Green" title="E53">A4</font></i>: 
<font color="Maroon" title="c2">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">R2</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E1:104_1_2"><i><font color="Green" title="E51">A2</font></i></a></i>;<br/>
<a NAME="E4:104_1_2"/>
<font color="Maroon" title="c3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">R1</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E2:104_1_2"><i><font color="Green" title="E52">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:104_1_2"/>
<font color="Maroon" title="c2">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">R2</font>
 <b>by </b><i><a class="txt" href="topgen_4.html#E3:104_1_2"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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