Corollary setoid_fun_choice_iff_simple_setoid_fun_choice :
  forall A B, SetoidFunctionalChoice_on A B <-> SimpleSetoidFunctionalChoice_on A B.

(* Specifications: *)
Theorem setoid_fun_choice_imp_fun_choice : forall A B, SetoidFunctionalChoice_on A B -> FunctionalChoice_on A B.