∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : CategoryTheory.Arrow (CategoryTheory.Arrow C)}
  (φ : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp X.left.hom ((CategoryTheory.Functor.id C).map φ.left.right) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id C).map φ.left.left) Y.left.hom