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<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">B</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><a NAME="E1:31_1_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:31_1_1_1"/>
 <a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">B</font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:31_1_1_1"/>
 <a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">A</font> is <a href="card_1.html#V1" target="_self">cardinal</a>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_1_1_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  holds <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">B</font> ) )
 ;<br/><a NAME="E2:31_1_1_2"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">A</font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#T42">ORDINAL1:42</a></i>;<br/><b>consider </b><font color="Maroon">L</font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><br/><a NAME="E4:31_1_1_2"/><i><font color="Green">E49</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">B</font>) ) )
 <b>from </b><i><a class="ref" href="ordinal2.html#S2">ORDINAL2:sch 2</a>();<br/></i><a NAME="E5:31_1_1_2"/>
 <a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="ordinal2.html#K4">sup</a> <font color="Maroon">L</font></span>)</span>
 <b>by </b><i>, , , </i>;<br/><b>hence </b><a NAME="E6:31_1_1_2"/>
 <a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">A</font> is   <a href="card_1.html#NM1">Cardinal</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:31_1_1"/>
 <a href="card_1.html#K3" target="_self">alef</a> <font color="Maroon">A</font> is <a href="card_1.html#V1" target="_self">cardinal</a>
 <b>by </b><i>, </i>;<br/>


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