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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ] <b>means </b>not <font color="Maroon">a<sub>1</sub></font> is <a href="moebius1.html#V1" target="_self">square-containing</a>;<br/>
<b>let </b><font color="Maroon">X1</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> , <font color="Maroon">X2</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:33_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">n</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/> ( <font color="Olive">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> iff not <font color="Olive">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> )
 <b>and </b><br/><a NAME="E2:33_1_2"/><i><font color="Green">E51</font></i>: 
for <font color="Olive">n</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <br/> ( <font color="Olive">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> iff not <font color="Olive">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a> )
 ;<br/>

<a NAME="E3:33_1_2"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">y</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] )
 
<b>by </b><i/>;<br/>
<a NAME="E4:33_1_2"/><i><font color="Green">E72</font></i>: 
for <font color="Olive">y</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] )
 
<b>by </b><i/>;<br/>
<a NAME="E5:33_1_2"/>
for <font color="Olive">X1</font>, <font color="Olive">X2</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a>   st ( for <font color="Olive">y</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] ) ) &amp; ( for <font color="Olive">y</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] ) ) holds <br/><font color="Olive">X1</font> <a href="hidden.html#R1">=</a> <font color="Olive">X2</font>
 
<b>from </b><i><a class="ref" href="subset_1.html#S2">SUBSET_1:sch 2</a>();<br/></i>
<b>hence </b><a NAME="E6:33_1_2"/>
<font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font>
 <b>by </b><i>, </i>;<br/>


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