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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">F</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> iff  <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Olive" title="b1">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> )</span><br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">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="c2">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> iff  <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> )</span><br/>



<a NAME="E1:2"/>
<font color="Maroon" title="c2">F</font>, <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="yellow_8.html#T4" title="YELLOW_8:th.4">YELLOW_8:4</a></i>;<br/>
<b>hence </b><a NAME="E2:2"/>
( <font color="Maroon" title="c2">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> iff  <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> )
 <b>by </b><i><a class="ref" href="yellow_8.html#T5" title="YELLOW_8:th.5">YELLOW_8:5</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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