(** [Z.abs_nat] and usual operations, statements with [Z.abs] *)

(* Specifications: *)
Lemma inj_succ_abs n : Z.abs_nat (Z.succ (Z.abs n)) = S (Z.abs_nat n).
Lemma inj_add_abs n m :
Z.abs_nat (Z.abs n + Z.abs m) = (Z.abs_nat n + Z.abs_nat m)%nat.
Lemma inj_mul_abs n m :
Z.abs_nat (Z.abs n * Z.abs m) = (Z.abs_nat n * Z.abs_nat m)%nat.