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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(** 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. *)
(** Statements of functional extensionality for simple and dependent functions. *)

(** Extensionality of [forall]s follows from functional extensionality. *)
Lemma forall_extensionality {A} {B C : A -> Type} (H : forall x : A, B x = C x)
: (forall x, B x) = (forall x, C x).