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<b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:52"/><i><font color="Green" title="E41">A1</font></i>: 
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">X</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b1">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> holds <br/><font color="Olive" title="b1">Y</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="card_4.html#D1" target="_self" title="CARD_4:def.1">CARD_4:def 1</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:52_1"/>
<font color="Maroon" title="c3">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 ;<br/><a NAME="E2:52_1"/><b>then </b>
<font color="Maroon" title="c3">Y</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a>
 <b>by </b><i><a class="txt" href="card_4.html#E1:52"><i><font color="Green" title="E41">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:52_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c3">Y</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="card_4.html#D1" target="_self" title="CARD_4:def.1">Def1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:52"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="card_4.html#E1:52"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="card_4.html#T54" target="_self" title="CARD_4:th.54">Th54</a>, <a class="ref" href="card_4.html#T60" target="_self" title="CARD_4:th.60">Th60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="card_4.html#D1" target="_self" title="CARD_4:def.1">CARD_4:def 1</a><br/>


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