(* Copyright (C) 2012  G. Gonthier, B. Ziliani, A. Nanevski, D. Dreyer  This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.  This program 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 General Public License for more details.  You should have received a copy of the GNU General Public License along with this program.  If not, see <http://www.gnu.org/licenses/>. *)
From mathcomp
From LemmaOverloading
From mathcomp
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(* uncomment for ssreflect trunk *)
Notation eqn_addl := eqn_add2l.
Notation modn_addl := modnDl.
Notation modn_mulr := modnMr.
Notation modn_add2m := modnDm.
Notation modn_addr := modnDr.
(*************)
(* Locations *)
(*************)
Inductive ptr := ptr_nat of nat.
Definition null := ptr_nat 0.
Definition nat_ptr (x : ptr) := let: ptr_nat y := x in y.
Definition eq_ptr (x y : ptr) :=
match x, y with ptr_nat m, ptr_nat n => m == n end.

(* Specifications: *)
Lemma eq_ptrP : Equality.axiom eq_ptr.
Lemma ptr_null x m : (x.+m == null) = (x == null) && (m == 0).
Definition ltn_ptr (x y : ptr) :=
match x, y with ptr_nat m, ptr_nat n => m < n end.
Lemma ltn_ptr_irr : irreflexive ltn_ptr.
End NullLemmas.