(** This file is part of the Flocq formalization of floating-point arithmetic in Coq: http://flocq.gforge.inria.fr/  Copyright (C) 2011-2013 Sylvie Boldo #<br /># Copyright (C) 2011-2013 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. *)
Section Zmissing.

(* Specifications: *)
(** About Z *)
Theorem Zopp_le_cancel :
forall x y : Z,
(-y <= -x)%Z -> Zle x y.
Theorem Zgt_not_eq :
forall x y : Z,
(y < x)%Z -> (x <> y)%Z.
(** About Z *)
Theorem Zopp_le_cancel :
forall x y : Z,
(-y <= -x)%Z -> Zle x y.
Theorem Zgt_not_eq :
forall x y : Z,
(y < x)%Z -> (x <> y)%Z.