Module Nat2Pos.
(** [Pos.of_nat] is a bijection between non-zero [nat] and [positive], with [Pos.to_nat] as reciprocal. See [Pos2Nat.id] above for the dual equation. *)

(** [Pos.of_nat] is hence injective for non-zero numbers *)
Lemma inj (n m : nat) : n<>0 -> m<>0 -> Pos.of_nat n = Pos.of_nat m -> n = m.