∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X Y : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ (CategoryTheory.Functor.id C) X Y)
      ((CategoryTheory.Functor.id C).map (β_ X Y).hom) =
    CategoryTheory.CategoryStruct.comp
      (β_ ((CategoryTheory.Functor.id C).obj X) ((CategoryTheory.Functor.id C).obj Y)).hom
      (CategoryTheory.Functor.LaxMonoidal.μ (CategoryTheory.Functor.id C) Y X)