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<b>let </b><font color="Maroon">n</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:54"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:54_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="moebius1.html#K3" target="_self">NatDivisors</a> <font color="Maroon">n</font>
 ;<br/><b>then consider </b><font color="Maroon">l</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:54_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">l</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 ;<br/><b>thus </b><a NAME="E4:54_1"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:54"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 ;<br/>

<b>hence </b><a NAME="E4:54"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="moebius1.html#K3" target="_self">NatDivisors</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="moebius1.html#E1"><i><font color="Green">Lemma36</font></i></a></i>;<br/>


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