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

<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B1</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> holds <br/>( <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b1">B1</font> is  <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a>  &amp; <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b1">B1</font> is  <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">B1</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> implies ( <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a>  &amp; <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:21"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c2">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a>  &amp; <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>  )</span><br/>

<a NAME="E2:21"/>
(  <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>  &amp;  <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_lar.html#T10" target="_self" title="CARD_LAR:th.10">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:21"/>
( <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V2" title="CARD_LAR:attr.2">closed</a>  &amp; <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">B1</font> is  <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="card_lar.html#T11" target="_self" title="CARD_LAR:th.11">Th12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
