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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: NUMBER01:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">s</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp;  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; (  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Olive" title="b1">s</font> holds <br/><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">n</font> ) holds <br/>( <font color="Olive" title="b2">n</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  iff <font color="Olive" title="b2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Olive" title="b1">s</font> )</div></div>
