(** This file is part of the Flocq formalization of floating-point arithmetic in Coq: http://flocq.gforge.inria.fr/  Copyright (C) 2010-2013 Sylvie Boldo #<br /># Copyright (C) 2010-2013 Guillaume Melquiond  This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.  This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the COPYING file for more details. *)
(** * Missing definitions/lemmas *)
Require Export Reals.
Require Export ZArith.
Require Export Fcore_Zaux.
Section Rmissing.

Theorem Rabs_minus_le:
forall x y : R,
(0 <= y)%R -> (y <= 2*x)%R ->
(Rabs (x-y) <= x)%R.