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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E29">Def3</font></span>   defines <a href="moebius1.html#K2" title="MOEBIUS1:func.2">Moebius</a> <a onclick="hs(this)" href="javascript:()">MOEBIUS1:def 3 : <br/></a><span> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( ( <font color="Olive" title="b1">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>  implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="moebius1.html#K2" title="MOEBIUS1:func.2">Moebius</a> <font color="Olive" title="b1">n</font> iff <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) ) &amp; (  not <font color="Olive" title="b1">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>  implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="moebius1.html#K2" title="MOEBIUS1:func.2">Moebius</a> <font color="Olive" title="b1">n</font> iff  ex <font color="Olive" title="b3">n9</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 <br/>( <font color="Olive" title="b3">n9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Olive" title="b3">n9</font></span>)</span></span>)</span></span>)</span> ) ) ) );<br/></span></div>
