From cfbfe13f5b515ae2e3c6cdd97e2ccee03bc26e56 Mon Sep 17 00:00:00 2001 From: Stephane Glondu Date: Sun, 1 Feb 2009 00:54:40 +0100 Subject: Imported Upstream version 8.2~rc2+dfsg --- theories/Numbers/Integer/Abstract/ZBase.v | 8 ++++---- theories/Numbers/Integer/Abstract/ZDomain.v | 4 ++-- theories/Numbers/Integer/Abstract/ZMulOrder.v | 6 +++--- theories/Numbers/Integer/BigZ/BigZ.v | 4 +--- theories/Numbers/Integer/BigZ/ZMake.v | 3 +-- theories/Numbers/Integer/NatPairs/ZNatPairs.v | 6 +++--- 6 files changed, 14 insertions(+), 17 deletions(-) (limited to 'theories/Numbers/Integer') diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v index 29e18548..0f71f2cc 100644 --- a/theories/Numbers/Integer/Abstract/ZBase.v +++ b/theories/Numbers/Integer/Abstract/ZBase.v @@ -8,7 +8,7 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZBase.v 11040 2008-06-03 00:04:16Z letouzey $ i*) +(*i $Id: ZBase.v 11674 2008-12-12 19:48:40Z letouzey $ i*) Require Export Decidable. Require Export ZAxioms. @@ -36,14 +36,14 @@ Proof NZpred_succ. Theorem Zeq_refl : forall n : Z, n == n. Proof (proj1 NZeq_equiv). -Theorem Zeq_symm : forall n m : Z, n == m -> m == n. +Theorem Zeq_sym : forall n m : Z, n == m -> m == n. Proof (proj2 (proj2 NZeq_equiv)). Theorem Zeq_trans : forall n m p : Z, n == m -> m == p -> n == p. Proof (proj1 (proj2 NZeq_equiv)). -Theorem Zneq_symm : forall n m : Z, n ~= m -> m ~= n. -Proof NZneq_symm. +Theorem Zneq_sym : forall n m : Z, n ~= m -> m ~= n. +Proof NZneq_sym. Theorem Zsucc_inj : forall n1 n2 : Z, S n1 == S n2 -> n1 == n2. Proof NZsucc_inj. diff --git a/theories/Numbers/Integer/Abstract/ZDomain.v b/theories/Numbers/Integer/Abstract/ZDomain.v index 15beb2b9..9a17e151 100644 --- a/theories/Numbers/Integer/Abstract/ZDomain.v +++ b/theories/Numbers/Integer/Abstract/ZDomain.v @@ -8,7 +8,7 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZDomain.v 10934 2008-05-15 21:58:20Z letouzey $ i*) +(*i $Id: ZDomain.v 11674 2008-12-12 19:48:40Z letouzey $ i*) Require Export NumPrelude. @@ -49,7 +49,7 @@ assert (x == y); [rewrite Exx'; now rewrite Eyy' | rewrite <- H2; assert (H3 : e x y); [now apply -> eq_equiv_e | now inversion H3]]]. Qed. -Theorem neq_symm : forall n m, n # m -> m # n. +Theorem neq_sym : forall n m, n # m -> m # n. Proof. intros n m H1 H2; symmetry in H2; false_hyp H2 H1. Qed. diff --git a/theories/Numbers/Integer/Abstract/ZMulOrder.v b/theories/Numbers/Integer/Abstract/ZMulOrder.v index e3f1d9aa..c7996ffd 100644 --- a/theories/Numbers/Integer/Abstract/ZMulOrder.v +++ b/theories/Numbers/Integer/Abstract/ZMulOrder.v @@ -8,7 +8,7 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZMulOrder.v 11040 2008-06-03 00:04:16Z letouzey $ i*) +(*i $Id: ZMulOrder.v 11674 2008-12-12 19:48:40Z letouzey $ i*) Require Export ZAddOrder. @@ -173,7 +173,7 @@ Notation Zmul_neg := Zlt_mul_0 (only parsing). Theorem Zle_0_mul : forall n m : Z, 0 <= n * m -> 0 <= n /\ 0 <= m \/ n <= 0 /\ m <= 0. Proof. -assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_symm). +assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_sym). intros n m. repeat rewrite Zlt_eq_cases. repeat rewrite R. rewrite Zlt_0_mul, Zeq_mul_0. pose proof (Zlt_trichotomy n 0); pose proof (Zlt_trichotomy m 0). tauto. @@ -184,7 +184,7 @@ Notation Zmul_nonneg := Zle_0_mul (only parsing). Theorem Zle_mul_0 : forall n m : Z, n * m <= 0 -> 0 <= n /\ m <= 0 \/ n <= 0 /\ 0 <= m. Proof. -assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_symm). +assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_sym). intros n m. repeat rewrite Zlt_eq_cases. repeat rewrite R. rewrite Zlt_mul_0, Zeq_mul_0. pose proof (Zlt_trichotomy n 0); pose proof (Zlt_trichotomy m 0). tauto. diff --git a/theories/Numbers/Integer/BigZ/BigZ.v b/theories/Numbers/Integer/BigZ/BigZ.v index cb920124..e5e950ac 100644 --- a/theories/Numbers/Integer/BigZ/BigZ.v +++ b/theories/Numbers/Integer/BigZ/BigZ.v @@ -8,7 +8,7 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id: BigZ.v 11282 2008-07-28 11:51:53Z msozeau $ i*) +(*i $Id: BigZ.v 11576 2008-11-10 19:13:15Z msozeau $ i*) Require Export BigN. Require Import ZMulOrder. @@ -104,8 +104,6 @@ exact sub_opp. exact add_opp. Qed. -Typeclasses unfold NZadd NZmul NZsub NZeq. - Add Ring BigZr : BigZring. (** Todo: tactic translating from [BigZ] to [Z] + omega *) diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v index 6305156b..98ad4c64 100644 --- a/theories/Numbers/Integer/BigZ/ZMake.v +++ b/theories/Numbers/Integer/BigZ/ZMake.v @@ -8,7 +8,7 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZMake.v 11282 2008-07-28 11:51:53Z msozeau $ i*) +(*i $Id: ZMake.v 11576 2008-11-10 19:13:15Z msozeau $ i*) Require Import ZArith. Require Import BigNumPrelude. @@ -30,7 +30,6 @@ Module Make (N:NType) <: ZType. | Neg : N.t -> t_. Definition t := t_. - Typeclasses unfold t. Definition zero := Pos N.zero. Definition one := Pos N.one. diff --git a/theories/Numbers/Integer/NatPairs/ZNatPairs.v b/theories/Numbers/Integer/NatPairs/ZNatPairs.v index 8b3d815d..9427b37b 100644 --- a/theories/Numbers/Integer/NatPairs/ZNatPairs.v +++ b/theories/Numbers/Integer/NatPairs/ZNatPairs.v @@ -8,7 +8,7 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZNatPairs.v 11040 2008-06-03 00:04:16Z letouzey $ i*) +(*i $Id: ZNatPairs.v 11674 2008-12-12 19:48:40Z letouzey $ i*) Require Import NSub. (* The most complete file for natural numbers *) Require Export ZMulOrder. (* The most complete file for integers *) @@ -110,7 +110,7 @@ Proof. unfold reflexive, Zeq. reflexivity. Qed. -Theorem ZE_symm : symmetric Z Zeq. +Theorem ZE_sym : symmetric Z Zeq. Proof. unfold symmetric, Zeq; now symmetry. Qed. @@ -127,7 +127,7 @@ Qed. Theorem NZeq_equiv : equiv Z Zeq. Proof. -unfold equiv; repeat split; [apply ZE_refl | apply ZE_trans | apply ZE_symm]. +unfold equiv; repeat split; [apply ZE_refl | apply ZE_trans | apply ZE_sym]. Qed. Add Relation Z Zeq -- cgit v1.2.3