apply lt_le_trans with (m := digit 1); auto with zarith.
apply digit_monotone.
generalize H'; case q; simpl in |- *; auto with zarith; intros q'; case q';
simpl in |- *; auto with zarith arith; intros; red in |- *;
simpl in |- *; red in |- *; intros; discriminate.
Qed.
Hint Resolve Zlt_gt: zarith.

Theorem digitAdd :
forall (q : Z) (r : nat),
q <> 0%Z -> digit (q * Zpower_nat n r) = digit q + r.