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authorGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
committerGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Logic/FunctionalExtensionality.v
parent6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff)
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/FunctionalExtensionality.v')
-rw-r--r--theories/Logic/FunctionalExtensionality.v14
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).