∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {A : C} [inst_2 : CategoryTheory.GrpObj A] (f : CategoryTheory.MonoidalCategoryStruct.tensorUnit C ⟶ A),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.id A)
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A) f))
        CategoryTheory.MonObj.mul)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.id A)
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A)
            (CategoryTheory.CategoryStruct.comp f CategoryTheory.GrpObj.inv)))
        CategoryTheory.MonObj.mul) =
    CategoryTheory.CategoryStruct.id A