∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (X Y Z : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv
      (CategoryTheory.CategoryStruct.comp
        {
            hom :=
              CategoryTheory.CartesianMonoidalCategory.lift
                (CategoryTheory.SemiCartesianMonoidalCategory.snd (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)
                  Z)
                (CategoryTheory.SemiCartesianMonoidalCategory.fst (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)
                  Z),
            inv :=
              CategoryTheory.CartesianMonoidalCategory.lift
                (CategoryTheory.SemiCartesianMonoidalCategory.snd Z
                  (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y))
                (CategoryTheory.SemiCartesianMonoidalCategory.fst Z
                  (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)),
            hom_inv_id := ⋯, inv_hom_id := ⋯ }.hom
        (CategoryTheory.MonoidalCategoryStruct.associator Z X Y).inv) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X
        {
            hom :=
              CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.SemiCartesianMonoidalCategory.snd Y Z)
                (CategoryTheory.SemiCartesianMonoidalCategory.fst Y Z),
            inv :=
              CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.SemiCartesianMonoidalCategory.snd Z Y)
                (CategoryTheory.SemiCartesianMonoidalCategory.fst Z Y),
            hom_inv_id := ⋯, inv_hom_id := ⋯ }.hom)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Z Y).inv
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight
          {
              hom :=
                CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.SemiCartesianMonoidalCategory.snd X Z)
                  (CategoryTheory.SemiCartesianMonoidalCategory.fst X Z),
              inv :=
                CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.SemiCartesianMonoidalCategory.snd Z X)
                  (CategoryTheory.SemiCartesianMonoidalCategory.fst Z X),
              hom_inv_id := ⋯, inv_hom_id := ⋯ }.hom
          Y))