(** * 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 Zquot_mult_le: forall a b c, 0<=a -> 0<=b -> 0<=c -> c*(a÷b) <= (c*a)÷b.