Fixpoint datDepth (A : Set)(t : DistApproxTree A) : nat :=
  match t with
    | dat_leaf o => O
    | dat_internal t1 t2 =>
      S (max (datDepth t1) (datDepth t2))
  end.

Lemma lowDistApprox_bind_div2_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 (fun n => lowDistApprox_bind c1 c2 a (div2 n)).