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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means <font color="Maroon">a<sub>1</sub></font> is <a href="int_2.html#V1">prime</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="E2:86_1_1"/><i><font color="Green">E47</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="nat_1.html#NM1">Nat</a>;<br/>

<b>thus </b><a NAME="E3:86_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 <font color="Maroon">c<sub>2</sub></font> is <a href="int_2.html#V1">prime</a> )
 <b>by </b><i><a class="txt" href="newton.html#E2:86_1_1"><i><font color="Green">E47</font></i></a></i>;<br/>

<b>assume </b><a NAME="E4:86_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="int_2.html#V1">prime</a>
 ;<br/>

<b>hence </b><a NAME="E5:86_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="newton.html#E2:86_1_1"><i><font color="Green">E47</font></i></a></i>;<br/>


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