
theorem Th9:
  for S, T being RelStr, f being Function of S, T st f is
  isomorphic holds f is onto
proof
  let S, T be RelStr, f be Function of S, T such that
A1: f is isomorphic;
  per cases;
  suppose
    S is non empty & T is non empty;
    hence rng f = the carrier of T by A1,WAYBEL_0:66;
  end;
  suppose
    S is empty or T is empty;
    then T is empty by A1,WAYBEL_0:def 38;
    then the carrier of T = {};
    hence rng f = the carrier of T;
  end;
end;
