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. *)
(** [Z.to_nat], basic equations *)
(** [Z.to_nat] and operations *)

Lemma inj_compare n m : 0<=n -> 0<=m ->
(Z.to_nat n ?= Z.to_nat m)%nat = (n ?= m).