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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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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 file provides classical logic and indefinite description under the form of Hilbert's epsilon operator *)
(** Hilbert's epsilon operator and classical logic implies excluded-middle in [Set] and leads to a classical world populated with non computable functions. It conflicts with the impredicativity of [Set] *)
Require Export Classical.
Set Implicit Arguments.
Opaque epsilon.
(** *** Weaker lemmas (compatibility lemmas) *)

Theorem choice :
forall (A B : Type) (R : A->B->Prop),
(forall x : A, exists y : B, R x y) ->
(exists f : A->B, forall x : A, R x (f x)).