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-rw-r--r--plugins/ring/LegacyNArithRing.v29
1 files changed, 13 insertions, 16 deletions
diff --git a/plugins/ring/LegacyNArithRing.v b/plugins/ring/LegacyNArithRing.v
index ae7e62e0..7f1597a1 100644
--- a/plugins/ring/LegacyNArithRing.v
+++ b/plugins/ring/LegacyNArithRing.v
@@ -1,13 +1,11 @@
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *)
+(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: LegacyNArithRing.v 14641 2011-11-06 11:59:10Z herbelin $ *)
-
(* Instantiation of the Ring tactic for the binary natural numbers *)
Require Import Bool.
@@ -16,7 +14,7 @@ Require Export ZArith_base.
Require Import NArith.
Require Import Eqdep_dec.
-Unboxed Definition Neq (n m:N) :=
+Definition Neq (n m:N) :=
match (n ?= m)%N with
| Datatypes.Eq => true
| _ => false
@@ -24,23 +22,22 @@ Unboxed Definition Neq (n m:N) :=
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.
+ apply N.compare_eq.
destruct (n ?= m)%N; [ reflexivity | contradiction | contradiction ].
Qed.
-Definition NTheory : Semi_Ring_Theory Nplus Nmult 1%N 0%N Neq.
+Definition NTheory : Semi_Ring_Theory N.add N.mul 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 N.add_comm.
+ apply N.add_assoc.
+ apply N.mul_comm.
+ apply N.mul_assoc.
+ apply N.add_0_l.
+ apply N.mul_1_l.
+ apply N.mul_0_l.
+ apply N.mul_add_distr_r.
apply Neq_prop.
Qed.
Add Legacy Semi Ring
- N Nplus Nmult 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ].
+ N N.add N.mul 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ].