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

Theorem simple_setoid_fun_choice_imp_setoid_fun_choice : forall A B, SimpleSetoidFunctionalChoice_on A B -> SetoidFunctionalChoice_on A B.