∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G) {X Y : D} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (F.map (G.map f)) (adj.counit.app Y) =
    CategoryTheory.CategoryStruct.comp (adj.counit.app X) f