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

<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">being_limit_ordinal</a> <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>

<b>thus </b><a NAME="E1:19"/>
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">A</font> is <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">B</font> be  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">being_limit_ordinal</a> <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="card_lar.html#D5" target="_self" title="CARD_LAR:def.5">CARD_LAR:def 5</a><br/>

<b>assume </b><a NAME="E1:19_1"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<b>assume </b><a NAME="E2:19_1"/>
 <a href="ordinal2.html#K3" title="ORDINAL2:func.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<b>thus </b><a NAME="E3:19_1"/>
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="card_lar.html#E1:19_1"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


</div><b>end;</b></div>

<a NAME="E2:19"/>
 <a href="ordinal2.html#K3" title="ORDINAL2:func.3">sup</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="ordinal2.html#T26" title="ORDINAL2:th.26">ORDINAL2:26</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
 <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">A</font> is <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>
 <b>by </b><i><a class="ref" href="card_lar.html#D4" target="_self" title="CARD_LAR:def.4">Def4</a></i>;<br/>


</div>
