Fixpoint Fix_F_sub (x : A) (r : Acc R x) : P x :=
    F_sub x (fun y: { y : A | R y x}  => Fix_F_sub (proj1_sig y)
      (Acc_inv r (proj2_sig y))).Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x).

(* Specifications: *)
Lemma Fix_F_inv : forall (x:A) (r s:Acc R x), Fix_F_sub x r = Fix_F_sub x s.
Lemma Fix_eq : forall x:A, Fix_sub x = F_sub x (fun y:{ y:A | R y x} => Fix_sub (proj1_sig y)).