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<b>let </b><font color="Maroon" title="c1">n</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:46"/>
not <font color="Maroon" title="c1">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">n'</font> being  non <a href="xxreal_0.html#NV4" title="XXREAL_0:NV.4">zero</a> <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E3:46"/><i><font color="Green" title="E33">A1</font></i>: 
( <font color="Maroon" title="c2">n'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="moebius1.html#K2" title="MOEBIUS1:func.2">Moebius</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> 1</span>)</span> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Maroon" title="c2">n'</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="moebius1.html#D3" target="_self" title="MOEBIUS1:def.3">Def3</a></i>;<br/>
<b>thus </b><a NAME="E4:46"/>
 <a href="moebius1.html#K2" title="MOEBIUS1:func.2">Moebius</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="moebius1.html#E3:46"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="card_4.html#T51" title="CARD_4:th.51">CARD_4:51</a></i>;<br/>


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