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 guarded_rel_choice_imp_rel_choice : forall A B : Type, GuardedRelationalChoice_on A B -> RelationalChoice_on A B.