Fixpoint Fix_F (x : A) (r : Acc R x) {struct r} : P x :=
  F x (fun (y : A) (p : R y x) => Fix_F y (Acc_inv r y p)).Scheme Acc_inv_dep := Induction for Acc Sort Prop.

(* Specifications: *)
Lemma Fix_F_eq : forall (x : A) (r : Acc R x), Fix_F x r = F x (fun (y : A) (p : R y x) => Fix_F y (Acc_inv r y p)).
Lemma Fix_F_inv : forall (x : A) (r s : Acc R x), Fix_F x r = Fix_F x s.