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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">T</font> holds   <a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Olive" title="b1">A</font> is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Maroon" title="c2">A</font> is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">T</font></span><br/>



<a NAME="E1:93"/>
<font color="Maroon" title="c2">A</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T6" title="FUNCT_2:th.6">FUNCT_2:6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">AA</font> =  <a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Maroon" title="c2">A</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<a NAME="E3:93"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font></span>)</span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font> is  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T80" title="CARD_2:th.80">CARD_2:80</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E4:93"/><span class="kw">then </span>
<font color="Maroon" title="c3">AA</font> is  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel12.html#T2" title="WAYBEL12:th.2">WAYBEL12:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:93"/>
 <a href="topgen_3.html#K1" title="TOPGEN_3:func.1">rng</a> <font color="Maroon" title="c2">A</font> is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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