fact: Definition proper_subtype_inclusion (U V : 𝒫 A) := (forall a, U a -> V a) /\ merely (exists a : A, V a /\ ~(U a)).
imports: HoTT(TruncType ExcludedMiddle Modalities.ReflectiveSubuniverse abstract_algebra HSet) HoTT(PropResizing.PropResizing) HoTT(Spaces.Card) HoTT.Sets(Ordinals Powers)