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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( $1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> &amp; $1 is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> );<br/>
<b>consider </b><font color="Maroon" title="c2">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:86_1_1"/><i><font color="Green" title="E49">A1</font></i>: 
for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">q</font>] )
 <b>from </b><i><a class="ref" href="subset_1.html#S3" title="SUBSET_1:sch.3">SUBSET_1:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c2">X</font>
;<br/>

<b>let </b><font color="Maroon" title="c3">q</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>thus </b><a NAME="E3:86_1_1"/>
( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies ( <font color="Maroon" title="c3">q</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c3">q</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> ) )
 <b>by </b><i><a class="txt" href="newton.html#E2:86_1_1"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>

<a NAME="E4:86_1_1"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>assume </b><a NAME="E5:86_1_1"/>
( <font color="Maroon" title="c3">q</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c3">q</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> )
 ;<br/>

<b>hence </b><a NAME="E6:86_1_1"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="txt" href="newton.html#E2:86_1_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="newton.html#E4:86_1_1"><i><font color="Green" title="E50">A2</font></i></a></i>;<br/>


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