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(** * Properties of absolute value *)

Notation Zabs_non_eq := Z.abs_neq (only parsing).Notation Zabs_Zopp := Z.abs_opp (only parsing).Notation Zabs_pos := Z.abs_nonneg (only parsing).Notation Zabs_eq_case := Z.abs_eq_cases (only parsing).Notation Zsgn_Zabs := Z.sgn_abs (only parsing).Notation Zabs_Zsgn := Z.abs_sgn (only parsing).Notation Zabs_Zmult := Z.abs_mul (only parsing).

(* Specifications: *)
Lemma Zabs_ind : forall (P:Z -> Prop) (n:Z), (n >= 0 -> P n) -> (n <= 0 -> P (- n)) -> P (Z.abs n).
Theorem Zabs_intro : forall P (n:Z), P (- n) -> P n -> P (Z.abs n).