∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {D : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] {L : CategoryTheory.Functor C D} {R : CategoryTheory.Functor D C}
  (h : L ⊣ R) ⦃X Y : C⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (L.map f) (CategoryTheory.CategoryStruct.id (L.obj Y)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id (L.obj X))
      (((CategoryTheory.Comonad.comparison h).comp h.toComonad.forget).map f)