assumption. assumption. omega. Qed.

Lemma Zdiv_mult_minus : forall a b m : Z, 0 < m -> 0 < b -> b <= m -> (a * m - b) / m = a - 1.
intros. replace (a * m - b) with ((a - 1) * m + (m - b)). apply Zdiv_mult_plus. auto. omega.