diff options
Diffstat (limited to 'theories/Sorting/PermutSetoid.v')
| -rw-r--r-- | theories/Sorting/PermutSetoid.v | 27 |
1 files changed, 10 insertions, 17 deletions
diff --git a/theories/Sorting/PermutSetoid.v b/theories/Sorting/PermutSetoid.v index 87b0b08d..2cd4f5f7 100644 --- a/theories/Sorting/PermutSetoid.v +++ b/theories/Sorting/PermutSetoid.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 *) (************************************************************************) -(*i $Id: PermutSetoid.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Import Omega Relations Multiset SetoidList. (** This file is deprecated, use [Permutation.v] instead. @@ -54,7 +52,7 @@ Lemma list_contents_app : forall l m:list A, meq (list_contents (l ++ m)) (munion (list_contents l) (list_contents m)). Proof. - simple induction l; simpl in |- *; auto with datatypes. + simple induction l; simpl; auto with datatypes. intros. apply meq_trans with (munion (singletonBag a) (munion (list_contents l0) (list_contents m))); @@ -67,19 +65,19 @@ Definition permutation (l m:list A) := meq (list_contents l) (list_contents m). Lemma permut_refl : forall l:list A, permutation l l. Proof. - unfold permutation in |- *; auto with datatypes. + unfold permutation; auto with datatypes. Qed. Lemma permut_sym : forall l1 l2 : list A, permutation l1 l2 -> permutation l2 l1. Proof. - unfold permutation, meq; intros; apply sym_eq; trivial. + unfold permutation, meq; intros; symmetry; trivial. Qed. Lemma permut_trans : forall l m n:list A, permutation l m -> permutation m n -> permutation l n. Proof. - unfold permutation in |- *; intros. + unfold permutation; intros. apply meq_trans with (list_contents m); auto with datatypes. Qed. @@ -104,7 +102,7 @@ Lemma permut_app : forall l l' m m':list A, permutation l l' -> permutation m m' -> permutation (l ++ m) (l' ++ m'). Proof. - unfold permutation in |- *; intros. + unfold permutation; intros. apply meq_trans with (munion (list_contents l) (list_contents m)); auto using permut_cons, list_contents_app with datatypes. apply meq_trans with (munion (list_contents l') (list_contents m')); @@ -344,8 +342,7 @@ Proof. rewrite if_eqA_refl in H. clear IHl; omega. rewrite IHl; intros. - specialize (H a0); auto with *. - destruct (eqA_dec a a0); simpl; auto with *. + specialize (H a0). omega. Qed. (** Permutation is compatible with InA. *) @@ -396,18 +393,14 @@ Proof. apply permut_length_1. red; red; intros. specialize (P a). simpl in *. - rewrite (@if_eqA_rewrite_l a1 a2 a) in P by auto. - (** Bug omega: le "set" suivant ne devrait pas etre necessaire *) - set (u:= if eqA_dec a2 a then 1 else 0) in *; omega. + rewrite (@if_eqA_rewrite_l a1 a2 a) in P by auto. omega. right. inversion_clear H0; [|inversion H]. split; auto. apply permut_length_1. red; red; intros. specialize (P a); simpl in *. - rewrite (@if_eqA_rewrite_l a1 b2 a) in P by auto. - (** Bug omega: idem *) - set (u:= if eqA_dec b2 a then 1 else 0) in *; omega. + rewrite (@if_eqA_rewrite_l a1 b2 a) in P by auto. omega. Qed. (** Permutation is compatible with length. *) @@ -492,7 +485,7 @@ Qed. End Permut_map. -Require Import Permutation TheoryList. +Require Import Permutation. Section Permut_permut. |