∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C} {κ : Cardinal.{w}}
  [inst_1 : Fact κ.IsRegular],
  P ≤ CategoryTheory.isCardinalPresentable C κ →
    (∀ (X : C), ∃ J x, ∃ (_ : CategoryTheory.IsCardinalFiltered J κ), P.colimitsOfShape J X) →
      P.IsCardinalFilteredGenerator κ