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<b>let </b><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/>

<b>thus </b><a NAME="E1:92"/>
<span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Olive">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> ) </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:92_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Olive">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">k1</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="E3:92_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k1</font> &amp; <font color="Maroon">k1</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Maroon">k1</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> )
 ;<br/>
<a NAME="E4:92_1"/>
<font color="Maroon">k1</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/>
<b>hence </b><a NAME="E5:92_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> ) </span>}</span> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:92"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a>  <a href="moebius1.html#K6" target="_self">Radical</a> <font color="Maroon">n</font> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">k1</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="E4:92"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k1</font> &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k1</font> &amp; <font color="Maroon">k1</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="E5:92"/>
 <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/>
<a NAME="E6:92"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">k1</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T51">NAT_1:51</a></i>;<br/>
<a NAME="E7:92"/>
not <font color="Maroon">k1</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:92"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> &amp; not <font color="Olive">k</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> ) </span>}</span> 
 <b>by </b><i>, </i>;<br/>


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