
theorem
  233 is prime
proof
  now
    233 = 2*116 + 1; hence not 2 divides 233 by NAT_4:9;
    233 = 3*77 + 2; hence not 3 divides 233 by NAT_4:9;
    233 = 5*46 + 3; hence not 5 divides 233 by NAT_4:9;
    233 = 7*33 + 2; hence not 7 divides 233 by NAT_4:9;
    233 = 11*21 + 2; hence not 11 divides 233 by NAT_4:9;
    233 = 13*17 + 12; hence not 13 divides 233 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 233 & n is prime
  holds not n divides 233 by XPRIMET1:12;
  hence thesis by NAT_4:14;
