(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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(** Properties of [abs] and [sgn] *)
(** Since we already have [max], we could have defined [abs]. *)
Module GenericAbs (Import Z : ZAxiomsMiniSig')
(Import ZP : ZMulOrderProp Z) <: HasAbs Z.
Definition abs n := max n (-n).

(* Specifications: *)
Lemma abs_eq : forall n, 0<=n -> abs n == n.
Lemma abs_neq : forall n, n<=0 -> abs n == -n.
End GenericAbs.