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

Lemma Fix_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 (Fix_F_sub A R P f y a)) -> forall (a: Acc R x), Q x (f (fun y: {y: A | R y x} => Fix_F_sub A R P f (proj1_sig y) (Acc_inv a (proj2_sig y))))) : forall x a, Q _ (Fix_F_sub A R P f x a).