intuition.
edestruct (dat_exists).
eauto.
rewrite <- low_tree_approx_same_inv; eauto.
eapply low_tree_approx_same_inv; eauto.
Grab Existential Variables.
eapply comp_eq_dec; eauto.
Qed.

Lemma lowDistApprox_bind_left_total : forall (A B : Set)(c1 : Comp B)(c2 : B -> Comp A) a,
well_formed_comp c1 ->
(forall b, In b (getSupport c1) -> well_formed_comp (c2 b)) ->
left_total (lowDistApprox_bind c1 c2 a).