intuition.
unfold lowDistApprox in *.
destruct H.
destruct H.
intuition.
rewrite H2.
eapply rat_le_1.
eapply le_trans.
eapply pred_count_le_length.
eapply H.
erewrite <- rel_map_length; eauto.
rewrite getAllBlists_length.
rattac.
Qed.

Theorem bind_low_tree_approx_same_inv : forall (A B : Set)(eqda : eq_dec A)(c1 : Comp B)(c2 : B -> Comp A) n a t r,
well_formed_comp c1 ->
(forall b, In b (getSupport c1) -> well_formed_comp (c2 b))->
lowDistApprox_bind c1 c2 a n r ->
dat_correct_bind2 c1 c2 n t ->
r == lowDistApproxFromTree eqda t a.