(** * Unicity results *)

Definition Remainder a b r :=
  (0 <= a /\ 0 <= r < Z.abs b) \/ (a <= 0 /\ -Z.abs b < r <= 0).Definition Remainder_alt a b r :=
  Z.abs r < Z.abs b /\ 0 <= r * a.

Theorem Zplus_rem: forall a b n, 0 <= a * b -> Z.rem (a + b) n = Z.rem (Z.rem a n + Z.rem b n) n.