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<b>reconsider </b><font color="Maroon" title="c2">E</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="ref" href="topgen_4.html#T18" target="_self" title="TOPGEN_4:th.18">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">Y</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><b> such that </b><br/><a NAME="E3:104_1_1"/><i><font color="Green" title="E51">A1</font></i>: 
( <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y</font> &amp; ( for <font color="Olive" title="b1">Z</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>  st <font color="Maroon" title="c2">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> holds <br/><font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> ) )
 <b>by </b><i><a class="ref" href="topgen_4.html#T67" target="_self" title="TOPGEN_4:th.67">Th67</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">Y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">G</font></span><br/>

<b>let </b><font color="Maroon" title="c4">G</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">G</font></span><br/>

<b>thus </b><a NAME="E4:104_1_1"/>
<font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="#E3:104_1_1"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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