(** Compatibility *)
Notation inj_Zabs_nat := Zabs2Nat.id_abs (only parsing).
Notation Zabs_nat_Z_of_nat := Zabs2Nat.id (only parsing).
Notation Zabs_nat_mult := Zabs2Nat.inj_mul (only parsing).
Notation Zabs_nat_Zsucc := Zabs2Nat.inj_succ (only parsing).
Notation Zabs_nat_Zplus := Zabs2Nat.inj_add (only parsing).
Notation Zabs_nat_Zminus := (fun n m => Zabs2Nat.inj_sub m n) (only parsing).
Notation Zabs_nat_compare := Zabs2Nat.inj_compare (only parsing).

(* Specifications: *)
Lemma Zabs_nat_le n m : 0 <= n <= m -> (Z.abs_nat n <= Z.abs_nat m)%nat.
Lemma Zabs_nat_lt n m : 0 <= n < m -> (Z.abs_nat n < Z.abs_nat m)%nat.