(************************************************************************)
(*         *      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)         *)
(************************************************************************)
(************)
Local Coercion inject_Z : Z >-> Q.
Definition Qfloor (x:Q) := let (n,d) := x in Z.div n (Zpos d).
Definition Qceiling (x:Q) := (-(Qfloor (-x)))%Z.

Lemma Qceiling_lt : forall x, (Qceiling x-1)%Z < x.
#[global]
Hint Resolve Qceiling_lt : qarith.