Module Z2Nat.
(** [Z.to_nat] is a bijection between non-negative [Z] and [nat], with [Pos.of_nat] as reciprocal. See [nat2Z.id] above for the dual equation. *)
(** [Z.to_nat] is hence injective for non-negative integers. *)

Lemma inj_iff n m : 0<=n -> 0<=m -> (Z.to_nat n = Z.to_nat m <-> n = m).