(** 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. *)
(** * Roundings: properties and/or functions *)
Section RND_prop.
Open Scope R_scope.

Theorem Rnd_DN_UP_sym :
forall F : R -> Prop,
( forall x, F x -> F (- x) ) ->
forall rnd1 rnd2 : R -> R,
Rnd_DN F rnd1 -> Rnd_UP F rnd2 ->
forall x, rnd1 (- x) = - rnd2 x.