
theorem
  19 is prime
proof
  now
    19 = 2*9 + 1; hence not 2 divides 19 by NAT_4:9;
    19 = 3*6 + 1; hence not 3 divides 19 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 19 & n is prime
  holds not n divides 19 by XPRIMET1:4;
  hence thesis by NAT_4:14;
