Corollary fun_choice_iff_rel_choice_and_functional_rel_reification :
  forall A B : Type, FunctionalChoice_on A B <->
    RelationalChoice_on A B /\ FunctionalRelReification_on A B.

Lemma rel_choice_indep_of_general_premises_imp_guarded_rel_choice : forall A B : Type, inhabited B -> RelationalChoice_on A B -> IndependenceOfGeneralPremises -> GuardedRelationalChoice_on A B.