(* 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.
(*************)
(* Locations *)
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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.
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.