∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] {κ : Cardinal.{u_1}} [Fact κ.IsRegular] {ι : Type u_2}
  (D : ι → CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram J κ),
  HasCardinalLT ι κ → (⨆ i, (D i).W).HasCardinalLT κ