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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E53">Th66</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: ORDINAL7:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="ordinal5.html#V1" title="ORDINAL5:attr.1">decreasing</a>  <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a><br/>  for <font color="Olive" title="b2">B</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a>  <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a>  st  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">B</font> holds <br/> ex <font color="Olive" title="b3">C</font> being   <a href="ordinal5.html#V6" title="ORDINAL5:attr.6">Cantor-normal-form</a>  <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a> st <br/>( <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K1" title="ORDINAL7:func.1">-exponent</a> <font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K3" title="ORDINAL7:func.3">-leading_coeff</a> <font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> )</div></div>
