∀ {C : Type u_5} [inst : CategoryTheory.Category.{u_6, u_5} C] {D : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_4, u_3} D] (F : CategoryTheory.Functor C D) [inst_2 : F.Initial] {E : Type u_2}
  [inst_3 : CategoryTheory.Category.{u_1, u_2} E] [inst_4 : CategoryTheory.Limits.HasLimitsOfShape D E]
  [inst_5 : CategoryTheory.Limits.HasLimitsOfShape C E] {X Y : CategoryTheory.Functor D E} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.lim.map f)
      ((fun G => (CategoryTheory.Functor.Initial.limitIso F G).symm) Y).hom =
    CategoryTheory.CategoryStruct.comp ((fun G => (CategoryTheory.Functor.Initial.limitIso F G).symm) X).hom
      ((((CategoryTheory.Functor.whiskeringLeft C D E).obj F).comp CategoryTheory.Limits.lim).map f)