Corollary setoid_fun_choice_iff_gen_setoid_fun_choice :
  forall A B, SetoidFunctionalChoice_on A B <-> GeneralizedSetoidFunctionalChoice_on A B.

(* Specifications: *)
Theorem setoid_fun_choice_imp_simple_setoid_fun_choice : forall A B, SetoidFunctionalChoice_on A B -> SimpleSetoidFunctionalChoice_on A B.
Theorem simple_setoid_fun_choice_imp_setoid_fun_choice : forall A B, SimpleSetoidFunctionalChoice_on A B -> SetoidFunctionalChoice_on A B.