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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: CARD_LAR:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <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#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">X</font> is  <a href="card_lar.html#V1" title="CARD_LAR:attr.1">unbounded</a>  &amp;  <a href="card_lar.html#K2" title="CARD_LAR:func.2">limpoints</a> <font color="Olive" title="b2">X</font> is  <a href="card_lar.html#NV3" title="CARD_LAR:NV.3">bounded</a>  holds <br/> ex <font color="Olive" title="b3">B1</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> st <br/>( <font color="Olive" title="b3">B1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b4">B2</font></span>)</span> where <font color="Olive" title="b4">B2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font> : ( <font color="Olive" title="b4">B2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> &amp; <font color="Olive" title="b3">B1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b4">B2</font> ) </span> } </span>  <a href="card_lar.html#R3" title="CARD_LAR:pred.3">is_club_in</a> <font color="Olive" title="b1">A</font> )</div></div>
