now :: thesis: not 2 divides 5

5 = (2 * 2) + 1 ;
hence not 2 divides 5 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 5 & n is prime holds
not n divides 5 by XPRIMET1:2;
hence 5 is prime by NAT_4:14; :: thesis: verum