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 *)

Lemma inj_iff a a' : N.to_nat a = N.to_nat a' <-> a = a'.