Module N2Z.
(** [Z.of_N] is a bijection between [N] and non-negative [Z], with [Z.to_N] (or [Z.abs_N]) as reciprocal. See [Z2N.id] below for the dual equation. *)
(** [Z.of_N] is hence injective *)
(** [Z.of_N] produce non-negative integers *)
(** [Z.of_N], basic equations *)
(** [Z.of_N] and usual operations. *)
(** [Z.to_N] is hence injective for non-negative integers. *)
(** [Z.to_N], basic equations *)
(** [Z.to_N] and operations *)

Lemma inj_rem n m :0<=n -> 0<=m ->
Z.to_N (Z.rem n m) = ((Z.to_N n) mod (Z.to_N m))%N.