induction 1; intuition.
inversion H0; clear H0; subst.
assert (ca_done a = ca_done a0).
eapply evalDet_func; eauto.
inversion H0.
econstructor.
econstructor.
specialize (H2 a).
intuition.
inversion H0; clear H0; subst.
specialize (H a).
intuition.
econstructor.
omega.
inversion H2; clear H2; subst.
specialize (H a).
intuition.
econstructor.
assert (n >= n0).
omega.
eauto with dat.
Qed.

(* Specifications: *)
Lemma lowDistApprox_dat_better_le : forall (A : Set)(eqd : eq_dec A)(t1 t2 : DistApproxTree A),
dat_better t1 t2 ->
forall (a : A),
lowDistApproxFromTree eqd t2 a <= lowDistApproxFromTree eqd t1 a.