(**************************************************************************)
(*                                                                        *)
(*  This file is part of WP plug-in of Frama-C.                           *)
(*                                                                        *)
(*  Copyright (C) 2007-2015                                               *)
(*    CEA (Commissariat a l'energie atomique et aux energies              *)
(*         alternatives)                                                  *)
(*                                                                        *)
(*  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, version 2.1.                                              *)
(*                                                                        *)
(*  It 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         *)
(*  GNU Lesser General Public License for more details.                   *)
(*                                                                        *)
(*  See the GNU Lesser General Public License version 2.1                 *)
(*  for more details (enclosed in the file licenses/LGPLv2.1).            *)
(*                                                                        *)
(**************************************************************************)

(* this is a prelude for Alt-Ergo*)
(** The theory BuiltIn_ must be appended to this file*)
(** The theory Bool_ must be appended to this file*)
(** The theory int_Int_ must be appended to this file*)
(** The theory int_Abs_ must be appended to this file*)
(** The theory real_Real_ must be appended to this file*)
(** The theory real_RealInfix_ must be appended to this file*)
(** The theory real_Square_ must be appended to this file*)
axiom abs_def : (forall x:int [abs_int(x)]. ((0 <= x) -> (abs_int(x) = x)))

axiom abs_def1 :
  (forall x:int [abs_int(x)]. ((not (0 <= x)) -> (abs_int(x) = (-x))))

axiom sqrt_lin1 : (forall x:real [sqrt(x)]. ((1.0 <  x) -> (sqrt(x) <  x)))

axiom sqrt_lin0 :
  (forall x:real [sqrt(x)]. (((0.0 <  x) and (x <  1.0)) -> (x <  sqrt(x))))

axiom sqrt_0 : (sqrt(0.0) = 0.0)

axiom sqrt_1 : (sqrt(1.0) = 1.0)

