fact: Hypothesis F_G_compat: forall S T:Ensemble X, In (filter_family F) S -> In (filter_family G) T -> Inhabited (Intersection S T).
imports: ZornsLemma(DecidableDec FiniteIntersections FunctionProperties) ZornsLemma(FiniteIntersections) ZornsLemma(ZornsLemma)