
theorem
  67 is prime
proof
  now
    67 = 2*33 + 1; hence not 2 divides 67 by NAT_4:9;
    67 = 3*22 + 1; hence not 3 divides 67 by NAT_4:9;
    67 = 5*13 + 2; hence not 5 divides 67 by NAT_4:9;
    67 = 7*9 + 4; hence not 7 divides 67 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 67 & n is prime
  holds not n divides 67 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
