∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.MonoidalCategory C}
  [self : CategoryTheory.BraidedCategory C] {X Y : C} (f : X ⟶ Y) (Z : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z) (β_ Y Z).hom =
    CategoryTheory.CategoryStruct.comp (β_ X Z).hom (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Z f)