
theorem
  for f being one-to-one UnOp of [.0,1.],
      d being Element of [.0,1.] st
    d in rng f holds (f").d in dom f
  proof
    let f be one-to-one UnOp of [.0,1.],
        d be Element of [.0,1.];
    set X = [.0,1.];
    reconsider fX = f|X as PartFunc of X, X;
    assume
a1: d in rng f;
YZ: dom f = rng (f") by FUNCT_1:33;
    reconsider dd = d as Element of REAL;
    dom (f") = rng f by FUNCT_1:33;
    hence thesis by YZ,FUNCT_1:3,a1;
  end;
