induction t; intuition; simpl in *.
inversion H0; clear H0; subst.
inversion H1; clear H1; subst.
econstructor.
inversion H1; clear H1; subst.
eapply H; eauto.
inversion H0; clear H0; subst.
inversion H1; clear H1; subst.
econstructor; eauto.
Qed.

(* Specifications: *)
Lemma datMap_depth_better : forall (A B : Set)(tb1 tb2 : DistApproxTree B),
dat_better tb1 tb2 ->
forall  n1 n2 (f : nat -> B -> DistApproxTree A -> Prop) t1 t2,
(forall n1 n2 b t1 t2, n1 >= n2 -> f n1 b t1 -> f n2 b t2 -> dat_better t1 t2) ->
datMap (f n1) tb1 t1 ->
datMap_depth f n2 tb2 t2 ->
n1 >= n2 ->
dat_better t1 t2.