Definition MR (x y: T): Prop := R (m x) (m y).

(* Specifications: *)
Lemma measure_wf: well_founded MR.
Lemma F_unfold x r: Wf.Fix_F_sub A R P f x r = f (fun y => Wf.Fix_F_sub A R P f (proj1_sig y) (Acc_inv r (proj2_sig y))).
Lemma F_sub_rect (Q: forall x, P x -> Type) (inv: forall x: A, (forall (y: A) (H: R y x) (a: Acc R y), Q y (Wf.Fix_F_sub A R P f y a)) -> forall (a: Acc R x), Q x (f (fun y: {y: A | R y x} => Wf.Fix_F_sub A R P f (proj1_sig y) (Acc_inv a (proj2_sig y))))) : forall x a, Q _ (Wf.Fix_F_sub A R P f x a).
Lemma eq_F_sub x: forall (a a': Acc R x), Wf.Fix_F_sub A R P f x a = Wf.Fix_F_sub A R P f x a'.
Lemma unfold x: Wf.Fix_sub A R Rwf P f x = f (fun y => Wf.Fix_sub A R Rwf P f (proj1_sig y)).
Lemma rect (Q: forall x, P x -> Type) (inv: forall (x: A) (H: forall (y: A), R y x -> Q y (Wf.Fix_sub A R Rwf P f y)) (a: Acc R x), Q x (f (fun y: {y: A | R y x} => Wf.Fix_sub A R Rwf P f (proj1_sig y)))) : forall x, Q _ (Wf.Fix_sub A R Rwf P f x).