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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th28</font></span>: <a NAME="T29"><span class="comment"><font color="firebrick">:: CARD_5:29</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a>  st  <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">a</font> holds <br/> ex <font color="Olive" title="b2">xi</font> being   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a> st <br/>(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">xi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Olive" title="b1">a</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">xi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">xi</font> is  <a href="ordinal2.html#V2" title="ORDINAL2:attr.2">increasing</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal2.html#K4" title="ORDINAL2:func.4">sup</a> <font color="Olive" title="b2">xi</font> &amp; <font color="Olive" title="b2">xi</font> is   <a href="card_3.html#NM1" title="CARD_3:NM.1">Cardinal-Function</a> &amp;  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">xi</font> )</div></div>
