∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) (J : Type u_1) [inst_1 : CategoryTheory.Category.{u_4, u_1} J]
  ⦃X Y : CategoryTheory.Arrow (CategoryTheory.Functor J C)⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Arrow.leftFunc.map f)
      { app := fun j => (data.factorizationData (Y.hom.app j)).i, naturality := ⋯ } =
    CategoryTheory.CategoryStruct.comp { app := fun j => (data.factorizationData (X.hom.app j)).i, naturality := ⋯ }
      ((CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z data J).map f)