Module N2Nat.
(** [N.to_nat] is a bijection between [N] and [nat], with [Pos.of_nat] as reciprocal. See [Nat2N.id] below for the dual equation. *)
(** [N.to_nat] is hence injective *)
(** Interaction of this translation and usual operations. *)

Lemma inj_max a a' :
N.to_nat (N.max a a') = Nat.max (N.to_nat a) (N.to_nat a').