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.

(* Specifications: *)
Lemma rel_choice_and_proof_irrel_imp_guarded_rel_choice : RelationalChoice -> ProofIrrelevance -> GuardedRelationalChoice.
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.
Lemma guarded_rel_choice_imp_rel_choice : forall A B : Type, GuardedRelationalChoice_on A B -> RelationalChoice_on A B.
Lemma subset_types_imp_guarded_rel_choice_iff_rel_choice : ProofIrrelevance -> (GuardedRelationalChoice <-> RelationalChoice).