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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E19">A1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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> )
 
<b>by </b><i><a class="ref" href="card_lar.html#T11" target="_self" title="CARD_LAR:th.11">Th11</a></i>;<br/>
<b>hence </b><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> )
 <b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="card_lar.html#T12" target="_self" title="CARD_LAR:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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