<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">a</font> being  <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">a</font> &amp;  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">a</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">a</font> )</span><br/>



<a NAME="E1:23"/>
(  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#T9" title="CARD_4:th.9">CARD_4:9</a>, <a class="ref" href="card_4.html#T11" title="CARD_4:th.11">CARD_4:11</a></i>;<br/>
<b>hence </b><a NAME="E2:23"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
