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authorGravatar letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-03-04 17:33:35 +0000
committerGravatar letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-03-04 17:33:35 +0000
commit58c70113a815a42593c566f64f2de840fc7e48a1 (patch)
treec667f773ad8084832e54cebe46e6fabe07a9adeb /theories/FSets/FSetProperties.v
parent1f559440d19d9e27a3c935a26b6c8447c2220654 (diff)
migration from Set to Type of FSet/FMap + some dependencies...
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10616 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/FSets/FSetProperties.v')
-rw-r--r--theories/FSets/FSetProperties.v16
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/FSets/FSetProperties.v b/theories/FSets/FSetProperties.v
index 93adf6790..f3da02a83 100644
--- a/theories/FSets/FSetProperties.v
+++ b/theories/FSets/FSetProperties.v
@@ -317,7 +317,7 @@ Module WProperties (Import E : DecidableType)(M : WSfun E).
*)
Lemma fold_0 :
- forall s (A : Set) (i : A) (f : elt -> A -> A),
+ forall s (A : Type) (i : A) (f : elt -> A -> A),
exists l : list elt,
NoDup l /\
(forall x : elt, In x s <-> InA E.eq x l) /\
@@ -338,7 +338,7 @@ Module WProperties (Import E : DecidableType)(M : WSfun E).
[fold_2]. *)
Lemma fold_1 :
- forall s (A : Set) (eqA : A -> A -> Prop)
+ forall s (A : Type) (eqA : A -> A -> Prop)
(st : Setoid_Theory A eqA) (i : A) (f : elt -> A -> A),
Empty s -> eqA (fold f s i) i.
Proof.
@@ -351,7 +351,7 @@ Module WProperties (Import E : DecidableType)(M : WSfun E).
Qed.
Lemma fold_2 :
- forall s s' x (A : Set) (eqA : A -> A -> Prop)
+ forall s s' x (A : Type) (eqA : A -> A -> Prop)
(st : Setoid_Theory A eqA) (i : A) (f : elt -> A -> A),
compat_op E.eq eqA f ->
transpose eqA f ->
@@ -371,7 +371,7 @@ Module WProperties (Import E : DecidableType)(M : WSfun E).
the initial element, it is Leibniz-equal to it. *)
Lemma fold_1b :
- forall s (A : Set)(i : A) (f : elt -> A -> A),
+ forall s (A : Type)(i : A) (f : elt -> A -> A),
Empty s -> (fold f s i) = i.
Proof.
intros.
@@ -479,7 +479,7 @@ Module WProperties (Import E : DecidableType)(M : WSfun E).
(** Other properties of [fold]. *)
Section Fold.
- Variables (A:Set)(eqA:A->A->Prop)(st:Setoid_Theory _ eqA).
+ Variables (A:Type)(eqA:A->A->Prop)(st:Setoid_Theory _ eqA).
Variables (f:elt->A->A)(Comp:compat_op E.eq eqA f)(Ass:transpose eqA f).
Section Fold_1.
@@ -972,7 +972,7 @@ Module OrdProperties (M:S).
(** More properties of [fold] : behavior with respect to Above/Below *)
Lemma fold_3 :
- forall s s' x (A : Set) (eqA : A -> A -> Prop)
+ forall s s' x (A : Type) (eqA : A -> A -> Prop)
(st : Setoid_Theory A eqA) (i : A) (f : elt -> A -> A),
compat_op E.eq eqA f ->
Above x s -> Add x s s' -> eqA (fold f s' i) (f x (fold f s i)).
@@ -989,7 +989,7 @@ Module OrdProperties (M:S).
Qed.
Lemma fold_4 :
- forall s s' x (A : Set) (eqA : A -> A -> Prop)
+ forall s s' x (A : Type) (eqA : A -> A -> Prop)
(st : Setoid_Theory A eqA) (i : A) (f : elt -> A -> A),
compat_op E.eq eqA f ->
Below x s -> Add x s s' -> eqA (fold f s' i) (fold f s (f x i)).
@@ -1010,7 +1010,7 @@ Module OrdProperties (M:S).
no need for [(transpose eqA f)]. *)
Section FoldOpt.
- Variables (A:Set)(eqA:A->A->Prop)(st:Setoid_Theory _ eqA).
+ Variables (A:Type)(eqA:A->A->Prop)(st:Setoid_Theory _ eqA).
Variables (f:elt->A->A)(Comp:compat_op E.eq eqA f).
Lemma fold_equal :