
theorem
  199 is prime
proof
  now
    199 = 2*99 + 1; hence not 2 divides 199 by NAT_4:9;
    199 = 3*66 + 1; hence not 3 divides 199 by NAT_4:9;
    199 = 5*39 + 4; hence not 5 divides 199 by NAT_4:9;
    199 = 7*28 + 3; hence not 7 divides 199 by NAT_4:9;
    199 = 11*18 + 1; hence not 11 divides 199 by NAT_4:9;
    199 = 13*15 + 4; hence not 13 divides 199 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 199 & n is prime
  holds not n divides 199 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
