(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
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(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the GNU General Public License as published by  *)
(*  the Free Software Foundation, either version 2 of the License, or  *)
(*  (at your option) any later version.  This file is also distributed *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
(** This file collects some axioms used throughout the CompCert development. *)
Require ClassicalFacts.
Require FunctionalExtensionality.
(** * Extensionality axioms *)
(** The [Require FunctionalExtensionality] gives us functional extensionality for dependent function types: *)
Proof @FunctionalExtensionality.functional_extensionality_dep.
(** and, as a corollary, functional extensionality for non-dependent functions: *)
Proof @FunctionalExtensionality.functional_extensionality.
(** For compatibility with earlier developments, [extensionality] is an alias for [functional_extensionality]. *)

Lemma extensionality:
forall {A B: Type} (f g : A -> B),  (forall x, f x = g x) -> f = g.