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. *)

Lemma inj_pred_max n : Z.of_N (N.pred n) = Z.max 0 (Z.pred (Z.of_N n)).