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(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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(*i $Id: RelationalChoice.v,v 1.3.2.2 2004/08/01 09:29:59 herbelin Exp $ i*)

(** This file axiomatizes the relational form of the axiom of choice *)

Axiom
  relational_choice :
    forall (A B:Type) (R:A -> B -> Prop),
      (forall x:A,  exists y : B, R x y) ->
       exists R' : A -> B -> Prop,
        (forall x:A,
            exists y : B,
             R x y /\ R' x y /\ (forall y':B, R' x y' -> y = y')).