diff options
| author |  Stephane Glondu <steph@glondu.net> | 2012-08-20 18:27:02 +0200 |
|---|---|---|
| committer | Stephane Glondu <steph@glondu.net> | 2012-08-20 18:27:02 +0200 |
| commit | 595aa062e10b8d7100ec2ad9b766f9e624e47295 (patch) | |
| tree | 963f9c948173de70209cba5828b372f184afc306 /theories/Sets/Multiset.v | |
| parent | ab08ae9f0f944d9f801c44e4ffd3e6b7fcf4b024 (diff) | |
| parent | e0d682ec25282a348d35c5b169abafec48555690 (diff) | |
Merge tag 'upstream/8.4dfsg' into experimental/master
Upstream version 8.4dfsg
Diffstat (limited to 'theories/Sets/Multiset.v')
| -rw-r--r-- | theories/Sets/Multiset.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Sets/Multiset.v b/theories/Sets/Multiset.v index 5f21335f..1d0abab8 100644 --- a/theories/Sets/Multiset.v +++ b/theories/Sets/Multiset.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 *) @@ -42,14 +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. @@ -59,12 +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. @@ -72,21 +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. @@ -94,7 +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. |