∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {J : Type u_3} [inst_1 : LinearOrder J]
  [inst_2 : OrderBot J] {X Y : C} {f : X ⟶ Y} [inst_3 : SuccOrder J] [inst_4 : WellFoundedLT J]
  (c : CategoryTheory.TransfiniteCompositionOfShape J f) (j : J) (i i' : ↑(Set.Iic j)) (φ : i ⟶ i'),
  CategoryTheory.CategoryStruct.comp ((⋯.functor.comp c.F).map φ) (c.F.map (CategoryTheory.homOfLE ⋯)) =
    CategoryTheory.CategoryStruct.comp (c.F.map (CategoryTheory.homOfLE ⋯))
      (((CategoryTheory.Functor.const ↑(Set.Iic j)).obj (c.F.obj j)).map φ)