(**********************************************************************)
(** ** AC_fun_setoid = AC_fun_setoid_gen = AC_fun_setoid_simple       *)

(* Specifications: *)
Theorem gen_setoid_fun_choice_imp_setoid_fun_choice  :
forall A B, GeneralizedSetoidFunctionalChoice_on A B -> SetoidFunctionalChoice_on A B.
Theorem setoid_fun_choice_imp_gen_setoid_fun_choice :
forall A B, SetoidFunctionalChoice_on A B -> GeneralizedSetoidFunctionalChoice_on A B.
Corollary setoid_fun_choice_iff_gen_setoid_fun_choice :
forall A B, SetoidFunctionalChoice_on A B <-> GeneralizedSetoidFunctionalChoice_on A B.
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.
Corollary setoid_fun_choice_iff_simple_setoid_fun_choice :
forall A B, SetoidFunctionalChoice_on A B <-> SimpleSetoidFunctionalChoice_on A B.