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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* $Id: NArithRing.v,v 1.5.2.1 2004/07/16 19:30:13 herbelin Exp $ *)
+
+(* Instantiation of the Ring tactic for the binary natural numbers *)
+
+Require Export Ring.
+Require Export ZArith_base.
+Require Import NArith.
+Require Import Eqdep_dec.
+
+Definition Neq (n m:N) :=
+  match (n ?= m)%N with
+  | Datatypes.Eq => true
+  | _ => false
+  end.
+
+Lemma Neq_prop : forall n m:N, Is_true (Neq n m) -> n = m.
+  intros n m H; unfold Neq in H.
+  apply Ncompare_Eq_eq.
+  destruct (n ?= m)%N; [ reflexivity | contradiction | contradiction ].
+Qed.
+
+Definition NTheory : Semi_Ring_Theory Nplus Nmult 1%N 0%N Neq.
+  split.
+    apply Nplus_comm.
+    apply Nplus_assoc.
+    apply Nmult_comm.
+    apply Nmult_assoc.
+    apply Nplus_0_l.
+    apply Nmult_1_l.
+    apply Nmult_0_l.
+    apply Nmult_plus_distr_r.
+    apply Nplus_reg_l.
+    apply Neq_prop.
+Qed.
+
+Add Semi Ring N Nplus Nmult 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ].
+\ No newline at end of file