intuition.
unfold dat_correct in *.
edestruct low_tree_approx_same_h.
eauto.
trivial.
destruct H1.
econstructor.
econstructor.
intuition.
simpl in *.
eauto.
eauto.
rewrite H4.
eapply eqRat_refl.
Qed.

Lemma lowDistApprox_left_total : forall (A : Set)(eqd : eq_dec A)(c : Comp A) a,
well_formed_comp c ->
left_total (lowDistApprox c a).