∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) {X Y : C} (f : X ⟶ Y), W₂ (data.p.app (CategoryTheory.Arrow.mk f))