
theorem
  223 is prime
proof
  now
    223 = 2*111 + 1; hence not 2 divides 223 by NAT_4:9;
    223 = 3*74 + 1; hence not 3 divides 223 by NAT_4:9;
    223 = 5*44 + 3; hence not 5 divides 223 by NAT_4:9;
    223 = 7*31 + 6; hence not 7 divides 223 by NAT_4:9;
    223 = 11*20 + 3; hence not 11 divides 223 by NAT_4:9;
    223 = 13*17 + 2; hence not 13 divides 223 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 223 & n is prime
  holds not n divides 223 by XPRIMET1:12;
  hence thesis by NAT_4:14;
