∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) {Z : C} (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.Limits.HasImage g]
  [inst_2 : CategoryTheory.Limits.HasImage (CategoryTheory.CategoryStruct.comp f g)] {Z_1 : C}
  (h : CategoryTheory.Limits.image g ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage (CategoryTheory.CategoryStruct.comp f g))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.preComp f g) h) =
    CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage g) h)