∀ {C : Type u₂} [inst : CategoryTheory.Category.{v₂, u₂} C] {D : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} D]
  {E : Type u₄} [inst_2 : CategoryTheory.Category.{v₄, u₄} E]
  (F : CategoryTheory.Functor D (CategoryTheory.Functor C E)) (k : C) {X Y : D} (f : X ⟶ Y),
  ((CategoryTheory.Functor.flipping.inverse.obj F).obj k).map f = (F.map f).app k