∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {κ : Cardinal.{w}} [inst_1 : Fact κ.IsRegular]
  [CategoryTheory.LocallySmall.{w, v, u} C] {P : CategoryTheory.ObjectProperty C}
  [CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P],
  P.IsCardinalFilteredGenerator κ → CategoryTheory.ObjectProperty.EssentiallySmall.{w + 1, v, u} ⊤