∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {D : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
  [inst_4 : CategoryTheory.BraidedCategory C] [inst_5 : CategoryTheory.BraidedCategory D]
  (F : CategoryTheory.Functor C D) [inst_6 : F.Braided] {X Y : CategoryTheory.Grp C} (Z : CategoryTheory.Grp C)
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.mapGrp.obj Z) (F.mapGrp.map f))
      ((CategoryTheory.Grp.fullyFaithfulForget₂Mon D).preimageIso
          (CategoryTheory.Functor.Monoidal.μIso F.mapMon Z.toMon Y.toMon)).hom =
    CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Grp.fullyFaithfulForget₂Mon D).preimageIso
          (CategoryTheory.Functor.Monoidal.μIso F.mapMon Z.toMon X.toMon)).hom
      (F.mapGrp.map (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Z f))