Corollary fun_choice_and_small_drinker_iff_omniscient_fun_choice :
  FunctionalChoiceOnInhabitedSet /\ SmallDrinker'sParadox
  <-> OmniscientFunctionalChoice.

Lemma classical_denumerable_description_imp_fun_choice : forall A:Type, FunctionalRelReification_on A nat -> forall R:A->nat->Prop, (forall x y, decidable (R x y)) -> FunctionalChoice_on_rel R.