∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {D : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_2, u_3} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) {X Y : Cᵒᵖ} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((F.op.comp CategoryTheory.coyoneda).map f)
      ((fun X => CategoryTheory.NatIso.ofComponents (fun Y => (adj.homEquiv (Opposite.unop X) Y).toIso) ⋯) Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun X => CategoryTheory.NatIso.ofComponents (fun Y => (adj.homEquiv (Opposite.unop X) Y).toIso) ⋯) X).hom
      ((CategoryTheory.coyoneda.comp ((CategoryTheory.Functor.whiskeringLeft D C (Type u_2)).obj G)).map f)