proposition: Theorem functional_rel_reification_and_repr_fun_choice_iff_setoid_fun_choice : FunctionalRelReification /\ RepresentativeFunctionalChoice <-> SetoidFunctionalChoice.
proof: Proof. split; intros. - now apply functional_rel_reification_and_repr_fun_choice_imp_setoid_fun_choice. - split. + now intros A B; apply setoid_fun_choice_imp_functional_rel_reification. + now apply setoid_fun_choice_imp_repr_fun_choice. Qed.
imports: RelationClasses Logic Wf_nat Decidable Setoid Arith ClassicalFacts PropExtensionalityFacts