diff options
Diffstat (limited to 'theories/Arith/Gt.v')
| -rw-r--r-- | theories/Arith/Gt.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Arith/Gt.v b/theories/Arith/Gt.v index 32f453e5..31b15507 100644 --- a/theories/Arith/Gt.v +++ b/theories/Arith/Gt.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <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 *) @@ -15,7 +15,7 @@ Definition gt (n m:nat) := m < n. Require Import Le. Require Import Lt. Require Import Plus. -Open Local Scope nat_scope. +Local Open Scope nat_scope. Implicit Types m n p : nat. @@ -47,7 +47,7 @@ Hint Immediate gt_S_n: arith v62. Theorem gt_S : forall n m, S n > m -> n > m \/ m = n. Proof. - intros n m H; unfold gt in |- *; apply le_lt_or_eq; auto with arith. + intros n m H; unfold gt; apply le_lt_or_eq; auto with arith. Qed. Lemma gt_pred : forall n m, m > S n -> pred m > n. @@ -110,23 +110,23 @@ Hint Resolve le_gt_S: arith v62. Theorem le_gt_trans : forall n m p, m <= n -> m > p -> n > p. Proof. - red in |- *; intros; apply lt_le_trans with m; auto with arith. + red; intros; apply lt_le_trans with m; auto with arith. Qed. Theorem gt_le_trans : forall n m p, n > m -> p <= m -> n > p. Proof. - red in |- *; intros; apply le_lt_trans with m; auto with arith. + red; intros; apply le_lt_trans with m; auto with arith. Qed. Lemma gt_trans : forall n m p, n > m -> m > p -> n > p. Proof. - red in |- *; intros n m p H1 H2. + red; intros n m p H1 H2. apply lt_trans with m; auto with arith. Qed. Theorem gt_trans_S : forall n m p, S n > m -> m > p -> n > p. Proof. - red in |- *; intros; apply lt_le_trans with m; auto with arith. + red; intros; apply lt_le_trans with m; auto with arith. Qed. Hint Resolve gt_trans_S le_gt_trans gt_le_trans: arith v62. @@ -142,7 +142,7 @@ Qed. Lemma plus_gt_reg_l : forall n m p, p + n > p + m -> n > m. Proof. - red in |- *; intros n m p H; apply plus_lt_reg_l with p; auto with arith. + red; intros n m p H; apply plus_lt_reg_l with p; auto with arith. Qed. Lemma plus_gt_compat_l : forall n m p, n > m -> p + n > p + m. |