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<b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="c2">A</font> is <a href="topgen_4.html#V5" title="TOPGEN_4:attr.5">F_sigma</a> implies <font color="Maroon" title="c2">A</font> is <a href="topgen_4.html#V8" title="TOPGEN_4:attr.8">Borel</a> )</span><br/>

<b>assume </b><a NAME="E1:109_1_1"/>
<font color="Maroon" title="c2">A</font> is <a href="topgen_4.html#V5" title="TOPGEN_4:attr.5">F_sigma</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> is <a href="topgen_4.html#V8" title="TOPGEN_4:attr.8">Borel</a></span><br/>

<b>then consider </b><font color="Maroon" title="c3">F</font> being  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a> <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</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="E3:109_1_1"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="ref" href="topgen_4.html#D6" target="_self" title="TOPGEN_4:def.6">Def6</a></i>;<br/>
<a NAME="E4:109_1_1"/>
<font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topgen_4.html#K5" title="TOPGEN_4:func.5">BorelSets</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="topgen_4.html#T68" target="_self" title="TOPGEN_4:th.68">Th68</a></i>;<br/>
<a NAME="E5:109_1_1"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_4.html#K5" title="TOPGEN_4:func.5">BorelSets</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="txt" href="#E3:109_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="topgen_4.html#D4" target="_self" title="TOPGEN_4:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:109_1_1"/>
<font color="Maroon" title="c2">A</font> is <a href="topgen_4.html#V8" title="TOPGEN_4:attr.8">Borel</a>
 <b>by </b><i><a class="ref" href="topgen_4.html#D12" target="_self" title="TOPGEN_4:def.12">Def12</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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