Corollary setoid_fun_choice_imp_functional_rel_reification :
  forall A B, SetoidFunctionalChoice_on A B -> FunctionalRelReification_on A B.

(* Specifications: *)
Theorem setoid_fun_choice_imp_repr_fun_choice : SetoidFunctionalChoice -> RepresentativeFunctionalChoice .
Theorem functional_rel_reification_and_repr_fun_choice_imp_setoid_fun_choice : FunctionalRelReification -> RepresentativeFunctionalChoice -> SetoidFunctionalChoice.
Theorem functional_rel_reification_and_repr_fun_choice_iff_setoid_fun_choice : FunctionalRelReification /\ RepresentativeFunctionalChoice <-> SetoidFunctionalChoice.
Theorem fun_choice_and_ext_functions_repr_and_excluded_middle_imp_setoid_fun_choice : FunctionalChoice -> ExtensionalFunctionRepresentative -> ExcludedMiddle -> RepresentativeFunctionalChoice.
Theorem setoid_functional_choice_first_characterization : FunctionalChoice /\ ExtensionalFunctionRepresentative /\ ExcludedMiddle <-> SetoidFunctionalChoice.
Theorem fun_choice_and_ext_pred_ext_and_proof_irrel_imp_setoid_fun_choice : FunctionalChoice -> ExtensionalPredicateRepresentative -> ProofIrrelevance -> RepresentativeFunctionalChoice.
Theorem setoid_functional_choice_second_characterization : FunctionalChoice /\ ExtensionalPredicateRepresentative /\ ProofIrrelevance <-> SetoidFunctionalChoice.