blob: 8981a46a518a09c9b3738e9bd30df270e094e526 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
(* Instantiation of the Ring tactic for the binary integers of ZArith *)
Require Export ArithRing.
Require Export ZArith_base.
Require Import Eqdep_dec.
Definition Zeq (x y:Z) :=
match (x ?= y)%Z with
| Datatypes.Eq => true
| _ => false
end.
Lemma Zeq_prop : forall x y:Z, Is_true (Zeq x y) -> x = y.
intros x y H; unfold Zeq in H.
apply Zcompare_Eq_eq.
destruct (x ?= y)%Z; [ reflexivity | contradiction | contradiction ].
Qed.
Definition ZTheory : Ring_Theory Zplus Zmult 1%Z 0%Z Zopp Zeq.
split; intros; eauto with zarith.
apply Zeq_prop; assumption.
Qed.
(* NatConstants and NatTheory are defined in Ring_theory.v *)
Add Ring Z Zplus Zmult 1%Z 0%Z Zopp Zeq ZTheory
[ Zpos Zneg 0%Z xO xI 1%positive ].
|
