intros p q; unfold Zlt in |- *; generalize (Zcompare_EGAL p q);
(CaseEq (p ?= q)%Z; simpl in |- *; auto).
intros H H0; case (Zcompare_Gt_Lt_antisym p q); auto.
Qed.

(* Specifications: *)
Theorem digitAuxLess :
forall (v r : Z) (q : positive),
match digitAux v r q with
| S r' => (Zpower_nat n r' * r <= v)%Z
| O => True
end.