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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E76">Th95</font></span>: <a NAME="T82"><span class="comment"><font color="firebrick">:: ORDINAL7:82</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> holds <br/> ( ( <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K1" title="ORDINAL7:func.1">-exponent</a> <span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> implies <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K1" title="ORDINAL7:func.1">-exponent</a> <span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) &amp; ( <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K1" title="ORDINAL7:func.1">-exponent</a> <span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> implies <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal5.html#K5" title="ORDINAL5:func.5">-exponent</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="ordinal7.html#K1" title="ORDINAL7:func.1">-exponent</a> <span class="p2">(<span class="default"><a href="ordinal7.html#K4" title="ORDINAL7:func.4">CantorNF</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) )</div></div>
