theorem
  for f being one-to-one PartFunc of C,D st d in rng f holds d = f/.(f"
  /.d) & d = (f*(f"))/.d
proof
  let f be one-to-one PartFunc of C,D;
  assume
A1: d in rng f;
  then d = ((f*f") qua Function).d & d in dom (f*f") by FUNCT_1:35,37;
  hence thesis by A1,Th11,PARTFUN1:def 6;
end;
