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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
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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. *)
Definition f_equal__functional_extensionality_dep_good
{A B f g} H a
: f_equal (fun h => h a) (@functional_extensionality_dep_good A B f g H) = H a.

Lemma eta_expansion {A B} (f : A -> B) : f = fun x => f x.