diff options
Diffstat (limited to 'theories/Logic/FunctionalExtensionality.v')
| -rw-r--r-- | theories/Logic/FunctionalExtensionality.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Logic/FunctionalExtensionality.v b/theories/Logic/FunctionalExtensionality.v index 31b633c25..bf29c63dd 100644 --- a/theories/Logic/FunctionalExtensionality.v +++ b/theories/Logic/FunctionalExtensionality.v @@ -13,7 +13,7 @@ (** The converse of functional extensionality. *) -Lemma equal_f : forall {A B : Type} {f g : A -> B}, +Lemma equal_f : forall {A B : Type} {f g : A -> B}, f = g -> forall x, f x = g x. Proof. intros. @@ -23,11 +23,11 @@ Qed. (** Statements of functional extensionality for simple and dependent functions. *) -Axiom functional_extensionality_dep : forall {A} {B : A -> Type}, - forall (f g : forall x : A, B x), +Axiom functional_extensionality_dep : forall {A} {B : A -> Type}, + forall (f g : forall x : A, B x), (forall x, f x = g x) -> f = g. -Lemma functional_extensionality {A B} (f g : A -> B) : +Lemma functional_extensionality {A B} (f g : A -> B) : (forall x, f x = g x) -> f = g. Proof. intros ; eauto using @functional_extensionality_dep. @@ -37,8 +37,8 @@ Qed. Tactic Notation "extensionality" ident(x) := match goal with - [ |- ?X = ?Y ] => - (apply (@functional_extensionality _ _ X Y) || + [ |- ?X = ?Y ] => + (apply (@functional_extensionality _ _ X Y) || apply (@functional_extensionality_dep _ _ X Y)) ; intro x end. @@ -51,7 +51,7 @@ Proof. extensionality x. reflexivity. Qed. - + Lemma eta_expansion {A B} (f : A -> B) : f = fun x => f x. Proof. intros A B f. apply (eta_expansion_dep f). |