∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} C] {D : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_2, u_4} D] [inst_2 : CategoryTheory.MonoidalCategory D]
  {X Y : CategoryTheory.Functor C (CategoryTheory.Mon D)} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse.comp
            CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor).map
        f)
      ((fun A =>
            CategoryTheory.NatIso.ofComponents
              (fun X =>
                {
                  hom :=
                    {
                      hom :=
                        CategoryTheory.CategoryStruct.id
                          (((CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse.comp
                                      CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor).obj
                                  A).obj
                              X).X,
                      isMonHom_hom := ⋯ },
                  inv :=
                    {
                      hom :=
                        CategoryTheory.CategoryStruct.id
                          (((CategoryTheory.Functor.id (CategoryTheory.Functor C (CategoryTheory.Mon D))).obj A).obj
                              X).X,
                      isMonHom_hom := ⋯ },
                  hom_inv_id := ⋯, inv_hom_id := ⋯ })
              ⋯)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun A =>
            CategoryTheory.NatIso.ofComponents
              (fun X =>
                {
                  hom :=
                    {
                      hom :=
                        CategoryTheory.CategoryStruct.id
                          (((CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse.comp
                                      CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor).obj
                                  A).obj
                              X).X,
                      isMonHom_hom := ⋯ },
                  inv :=
                    {
                      hom :=
                        CategoryTheory.CategoryStruct.id
                          (((CategoryTheory.Functor.id (CategoryTheory.Functor C (CategoryTheory.Mon D))).obj A).obj
                              X).X,
                      isMonHom_hom := ⋯ },
                  hom_inv_id := ⋯, inv_hom_id := ⋯ })
              ⋯)
          X).hom
      ((CategoryTheory.Functor.id (CategoryTheory.Functor C (CategoryTheory.Mon D))).map f)