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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E58">Th49</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: NUMBER15:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">s</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">k</font>, <font color="Olive" title="b3">w</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Olive" title="b3">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Olive" title="b3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">k</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="number15.html#K5" title="NUMBER15:func.5">to_power</a> <span class="p2">(<span class="default"><a href="number15.html#K4" title="NUMBER15:func.4">sequenceA</a> <font color="Olive" title="b1">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="number15.html#K5" title="NUMBER15:func.5">to_power</a> <span class="p3">(<span class="default"><a href="number15.html#K9" title="NUMBER15:func.9">sequenceAnPk</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">k</font>)</span>)</span></span>)</span> <a href="nat_3.html#K1" title="NAT_3:func.1">|^</a> <span class="p2">(<span class="default"><a href="newton.html#K10" title="NEWTON:func.10">primenumber</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">w</font></div></div>
