∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (X Y : C),
  CategoryTheory.CategoryStruct.comp
      ({
            app := fun Z =>
              CategoryTheory.Over.homMk
                (CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.id Z.left) Z.hom) ⋯,
            naturality := ⋯ }.app
        ((CategoryTheory.toOver X).obj Y))
      ((CategoryTheory.toOver X).map
        ({ app := fun Z => CategoryTheory.SemiCartesianMonoidalCategory.fst Z X, naturality := ⋯ }.app Y)) =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.toOver X).obj Y)