Ltac nat2N := apply N2Nat.inj; now autorewrite with Nnat.
(** [N.of_nat] is hence injective *)

(* Specifications: *)
Lemma inj n n' : N.of_nat n = N.of_nat n' -> n = n'.
Lemma inj_iff n n' : N.of_nat n = N.of_nat n' <-> n = n'.
(** Interaction of this translation and usual operations. *)
Lemma inj_double n : N.of_nat (2*n) = N.double (N.of_nat n).