Corollary fun_choice_and_indep_general_prem_iff_guarded_fun_choice :
  FunctionalChoiceOnInhabitedSet /\ IndependenceOfGeneralPremises
  <-> GuardedFunctionalChoice.

Lemma omniscient_fun_choice_imp_fun_choice : OmniscientFunctionalChoice -> FunctionalChoiceOnInhabitedSet.