∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) {X Y X' Y' : C} {f : X ⟶ Y} {g : X' ⟶ Y'}
  (φ : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk g) {Z : C} (h : Y' ⟶ Z),
  CategoryTheory.CategoryStruct.comp (data.mapZ φ) (CategoryTheory.CategoryStruct.comp (data.factorizationData g).p h) =
    CategoryTheory.CategoryStruct.comp (data.factorizationData f).p (CategoryTheory.CategoryStruct.comp φ.right h)