∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {D : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_4, u_3} D] {F F' : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj1 : F ⊣ G) (adj2 : 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 => ((adj1.homEquiv (Opposite.unop X) Y).trans (adj2.homEquiv (Opposite.unop X) Y).symm).toIso) ⋯)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun X =>
            CategoryTheory.NatIso.ofComponents
              (fun Y => ((adj1.homEquiv (Opposite.unop X) Y).trans (adj2.homEquiv (Opposite.unop X) Y).symm).toIso) ⋯)
          X).hom
      ((F'.op.comp CategoryTheory.coyoneda).map f)