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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Y</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">Y</font> is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Olive" title="b1">Y</font></span>)</span> #)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Y</font> is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Maroon" title="c2">Y</font></span>)</span> #)</span><br/>



<a NAME="E1:27"/>
<font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cantor_1.html#T1" target="_self" title="CANTOR_1:th.1">Th1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:27"/>
<font color="Maroon" title="c2">Y</font> is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Maroon" title="c2">Y</font></span>)</span> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#T78" title="TOPS_2:th.78">TOPS_2:78</a>, <a class="ref" href="cantor_1.html#D2" target="_self" title="CANTOR_1:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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