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-rw-r--r--plugins/ring/LegacyNArithRing.v43
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-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-(* Instantiation of the Ring tactic for the binary natural numbers *)
-
-Require Import Bool.
-Require Export LegacyRing.
-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 N.compare_eq.
- destruct (n ?= m)%N; [ reflexivity | contradiction | contradiction ].
-Qed.
-
-Definition NTheory : Semi_Ring_Theory N.add N.mul 1%N 0%N Neq.
- split.
- 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 N.add N.mul 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ].