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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
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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 a limited form axiom of functional extensionality which selects a canonical representative in each class of extensional functions *)
(** Its main interest is that it is the needed ingredient to provide axiom of choice on setoids (a.k.a. axiom of extensional choice) when combined with classical logic and axiom of (intensonal) choice *)
(** It provides extensionality of functions while still supporting (a priori) an intensional interpretation of equality *)

(* Specifications: *)
Axiom extensional_function_representative :
forall A B, exists repr, forall (f : A -> B),
(forall x, f x = repr f x) /\
(forall g, (forall x, f x = g x) -> repr f = repr g).