∀ (C : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} C] (D : Type u₂) [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {X Y : CategoryTheory.Functor C D} (τ : X ⟶ Y) (f : CategoryTheory.Arrow C),
  (((CategoryTheory.Functor.mapArrowFunctor C D).map τ).app f).left = τ.app ((CategoryTheory.Functor.id C).obj f.left)