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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    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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Require Export QArith.
Require Export Qreduction.
Hint Resolve Qlt_le_weak : qarith.
Definition Qabs (x:Q) := let (n,d):=x in (Z.abs n#d).

Lemma Qabs_case : forall (x:Q) (P : Q -> Type), (0 <= x -> P x) -> (x <= 0 -> P (- x)) -> P (Qabs x).