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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> ) </span>}</span> ;<br/>
<b>assume </b><a NAME="E2:96"/>
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> ) </span>}</span>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:96"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> ) </span>}</span> 
 
;<br/>
<a NAME="E4:96"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> )
 
;<br/>
<a NAME="E5:96"/><b>then </b>
( 0 is <a href="int_2.html#V1">prime</a> or 1 is <a href="int_2.html#V1">prime</a> )
 
<b>by </b><i><a class="txt" href="newton.html#E93"><i><font color="Green">Lemma51</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:96"/>
contradiction
 <b>by </b><i><a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>


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