Axiom constructive_indefinite_description :
  forall (A : Type) (P : A->Prop),
    (exists x, P x) -> { x : A | P x }.

Lemma functional_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)).