diff options
Diffstat (limited to 'theories/Sets/Multiset.v')
| -rw-r--r-- | theories/Sets/Multiset.v | 20 |
1 files changed, 9 insertions, 11 deletions
diff --git a/theories/Sets/Multiset.v b/theories/Sets/Multiset.v index 6187c08b..1d0abab8 100644 --- a/theories/Sets/Multiset.v +++ b/theories/Sets/Multiset.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: Multiset.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - (* G. Huet 1-9-95 *) Require Import Permut Setoid. @@ -44,14 +42,14 @@ Section multiset_defs. Lemma meq_trans : forall x y z:multiset, meq x y -> meq y z -> meq x z. Proof. - unfold meq in |- *. + unfold meq. destruct x; destruct y; destruct z. intros; rewrite H; auto. Qed. Lemma meq_sym : forall x y:multiset, meq x y -> meq y x. Proof. - unfold meq in |- *. + unfold meq. destruct x; destruct y; auto. Qed. @@ -61,12 +59,12 @@ Section multiset_defs. Lemma munion_empty_left : forall x:multiset, meq x (munion EmptyBag x). Proof. - unfold meq in |- *; unfold munion in |- *; simpl in |- *; auto. + unfold meq; unfold munion; simpl; auto. Qed. Lemma munion_empty_right : forall x:multiset, meq x (munion x EmptyBag). Proof. - unfold meq in |- *; unfold munion in |- *; simpl in |- *; auto. + unfold meq; unfold munion; simpl; auto. Qed. @@ -74,21 +72,21 @@ Section multiset_defs. Lemma munion_comm : forall x y:multiset, meq (munion x y) (munion y x). Proof. - unfold meq in |- *; unfold multiplicity in |- *; unfold munion in |- *. + unfold meq; unfold multiplicity; unfold munion. destruct x; destruct y; auto with arith. Qed. Lemma munion_ass : forall x y z:multiset, meq (munion (munion x y) z) (munion x (munion y z)). Proof. - unfold meq in |- *; unfold munion in |- *; unfold multiplicity in |- *. + unfold meq; unfold munion; unfold multiplicity. destruct x; destruct y; destruct z; auto with arith. Qed. Lemma meq_left : forall x y z:multiset, meq x y -> meq (munion x z) (munion y z). Proof. - unfold meq in |- *; unfold munion in |- *; unfold multiplicity in |- *. + unfold meq; unfold munion; unfold multiplicity. destruct x; destruct y; destruct z. intros; elim H; auto with arith. Qed. @@ -96,7 +94,7 @@ Section multiset_defs. Lemma meq_right : forall x y z:multiset, meq x y -> meq (munion z x) (munion z y). Proof. - unfold meq in |- *; unfold munion in |- *; unfold multiplicity in |- *. + unfold meq; unfold munion; unfold multiplicity. destruct x; destruct y; destruct z. intros; elim H; auto. Qed. |