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_succ_double a : N.to_nat (N.succ_double a) = S (2*(N.to_nat a)).