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-rw-r--r--theories/Logic/FunctionalExtensionality.v18
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Logic/FunctionalExtensionality.v b/theories/Logic/FunctionalExtensionality.v
index 0dc82907..1678a287 100644
--- a/theories/Logic/FunctionalExtensionality.v
+++ b/theories/Logic/FunctionalExtensionality.v
@@ -6,14 +6,14 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: FunctionalExtensionality.v 11686 2008-12-16 12:57:26Z msozeau $ i*)
+(*i $Id$ i*)
(** This module states the axiom of (dependent) functional extensionality and (dependent) eta-expansion.
It introduces a tactic [extensionality] to apply the axiom of extensionality to an equality goal. *)
(** 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.
@@ -51,8 +51,8 @@ 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).
+ apply (eta_expansion_dep f).
Qed.