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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 1.1.2.1 2004/07/16 19:30:18 herbelin Exp $ *)
+
+(* Instantiation of the Ring tactic for the binary natural numbers *)
+
+Require Export Ring.
+Require Export ZArith_base.
+Require NArith.
+Require Eqdep_dec.
+
+Definition Neq := [n,m:entier]
+  Cases (Ncompare n m) of
+    EGAL => true
+  | _ => false
+  end.
+
+Lemma Neq_prop : (n,m:entier)(Is_true (Neq n m)) -> n=m.
+  Intros n m H; Unfold Neq in H.
+  Apply Ncompare_Eq_eq.
+  NewDestruct (Ncompare n m); [Reflexivity | Contradiction | Contradiction ].
+Save.
+
+Definition NTheory : (Semi_Ring_Theory Nplus Nmult (Pos xH) Nul 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.
+Save.
+
+Add Semi Ring entier Nplus Nmult (Pos xH) Nul Neq NTheory [Pos Nul xO xI xH].