Fixpoint Fix_F (x:A) (a:Acc x) : P x :=
    F (fun (y:A) (h:R y x) => Fix_F (Acc_inv a h)).Scheme Acc_inv_dep := Induction for Acc Sort Prop.

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