
theorem
  193 is prime
proof
  now
    193 = 2*96 + 1; hence not 2 divides 193 by NAT_4:9;
    193 = 3*64 + 1; hence not 3 divides 193 by NAT_4:9;
    193 = 5*38 + 3; hence not 5 divides 193 by NAT_4:9;
    193 = 7*27 + 4; hence not 7 divides 193 by NAT_4:9;
    193 = 11*17 + 6; hence not 11 divides 193 by NAT_4:9;
    193 = 13*14 + 11; hence not 13 divides 193 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 193 & n is prime
  holds not n divides 193 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
