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<b>let </b><font color="Maroon">k</font> be  non <a href="xboole_0.html#V1">zero</a> <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">zero</a> <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:91"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">k</font> is  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  &amp; <font color="Maroon">n</font> is  non <a href="xboole_0.html#V1">zero</a>  <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/>
<a NAME="E2:91"/>
( <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> implies ( <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Maroon">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E2:91_1"/>
 <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:91_1"/>
( <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Maroon">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> )
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T51">NAT_1:51</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91"/>
( ( <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Maroon">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> ) iff <font color="Maroon">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> )
 <b>by </b><i>, </i>;<br/>


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