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authorGravatar Stephane Glondu <steph@glondu.net>2012-08-20 18:27:01 +0200
committerGravatar Stephane Glondu <steph@glondu.net>2012-08-20 18:27:01 +0200
commite0d682ec25282a348d35c5b169abafec48555690 (patch)
tree1a46f0142a85df553388c932110793881f3af52f /theories/Sets/Multiset.v
parent86535d84cc3cffeee1dcd8545343f234e7285530 (diff)
Imported Upstream version 8.4dfsgupstream/8.4dfsg
Diffstat (limited to 'theories/Sets/Multiset.v')
-rw-r--r--theories/Sets/Multiset.v18
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.