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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: ORDINAL5:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a>  st 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">a</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  &amp; (  for <font color="Olive" title="b3">b</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="ordinal5.html#K1" title="ORDINAL5:func.1">|^|^</a> <font color="Olive" title="b3">b</font> ) holds <br/><font color="Olive" title="b2">f</font> is  <a href="ordinal2.html#V2" title="ORDINAL2:attr.2">increasing</a> </div></div>
