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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> ] means not <font color="Maroon">a<sub>1</sub></font> is <a href="moebius1.html#V1" target="_self">square-containing</a>;<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:33_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 <b>from </b><i><a class="ref" href="subset_1.html#S3">SUBSET_1:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon">c<sub>1</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E3:33_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>thus </b><a NAME="E4:33_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> implies  not <font color="Maroon">c<sub>2</sub></font> is <a href="moebius1.html#V1" target="_self">square-containing</a> )
 <b>by </b><i><a class="txt" href="moebius1.html#E2:33_1_1"><i><font color="Green">E24</font></i></a></i>;<br/>

<b>assume </b><a NAME="E5:33_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 ;<br/>

<b>hence </b><a NAME="E6:33_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="moebius1.html#E2:33_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="moebius1.html#E3:33_1_1"><i><font color="Green">E25</font></i></a></i>;<br/>


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