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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id: ClassicalChoice.v,v 1.1.2.1 2004/07/16 19:31:29 herbelin Exp $ i*)
(** This file provides classical logic and functional choice *)
(** This file extends ClassicalDescription.v with the axiom of choice.
As ClassicalDescription.v, it implies the double-negation of
excluded-middle in Set and implies a strongly classical
world. Especially it conflicts with impredicativity of Set, knowing
that true<>false in Set.
*)
Require Export ClassicalDescription.
Require Export RelationalChoice.
Require ChoiceFacts.
Theorem choice :
(A:Type;B:Type;R: A->B->Prop)
((x:A)(EX y:B|(R x y))) -> (EX f:A->B | (x:A)(R x (f x))).
Proof.
Apply description_rel_choice_imp_funct_choice.
Exact description.
Exact relational_choice.
Qed.
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