∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {κ : Cardinal.{w}} [inst_1 : Fact κ.IsRegular]
  [CategoryTheory.Limits.HasColimitsOfSize.{w, w, v, u} C] [CategoryTheory.LocallySmall.{w, v, u} C]
  {P : CategoryTheory.ObjectProperty C} [CategoryTheory.ObjectProperty.Small.{w, v, u} P],
  P.IsStrongGenerator →
    P ≤ CategoryTheory.isCardinalPresentable C κ →
      CategoryTheory.isCardinalPresentable C κ = P.colimitsCardinalClosure κ