theorem Th8:
  for f being Function of REAL,REAL holds f is Function of R^1, R^1
proof
  let f be Function of REAL,REAL;
  dom f = REAL by FUNCT_2:def 1;
  then reconsider B = rng f as non empty Subset of REAL by RELAT_1:42;
  f is Function of R^1, R^1 | R^1(B) by Th7;
  hence thesis by TOPREALA:7;
end;
