reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th7:
  for f being Function of REAL,REAL holds f is Function of R^1, R^1
  | R^1(rng f)
proof
  let f be Function of REAL,REAL;
  REAL = dom f by FUNCT_2:def 1;
  then R^1 | R^1(dom f) = R^1 by Th6;
  then R^1(f) is Function of R^1, R^1 | R^1(rng f);
  hence thesis;
end;
