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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** Binary Integers : properties of absolute value *)
(** Initial author : Pierre Crégut (CNET, Lannion, France) *)
(** THIS FILE IS DEPRECATED. It is now almost entirely made of compatibility formulations for results already present in BinInt.Z. *)
Local Open Scope Z_scope.
(**********************************************************************)
(** * 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).
(** * Proving a property of the absolute value by cases *)

Theorem Zabs_intro : forall P (n:Z), P (- n) -> P n -> P (Z.abs n).