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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E54">Def10</font></span>   defines <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <a onclick="hs(this)" href="javascript:()">ORDINAL5:def 10 : <br/></a><span> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive">b<sub>3</sub></font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> holds <br/> ( ( 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">b</font> &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">a</font> implies ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Olive" title="b1">a</font> iff (  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<font color="Olive" title="b2">b</font>,<font color="Olive">b<sub>3</sub></font>) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">a</font> &amp; (  for <font color="Olive" title="b4">c</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st  <a href="ordinal2.html#K12" title="ORDINAL2:func.12">exp</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">c</font>) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Olive" title="b4">c</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive">b<sub>3</sub></font> ) ) ) ) &amp; ( (  not 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">b</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">a</font> ) implies ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <font color="Olive" title="b1">a</font> iff <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) ) );<br/></span></div>
