∀ {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' X : C} {Y Y' : D} (f : X' ⟶ X)
  (g : X ⟶ G.obj Y') (h : X' ⟶ G.obj Y) (k : Y ⟶ Y'),
  CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.comp h (G.map k) →
    CategoryTheory.CategoryStruct.comp (F.map f) ((adj.homEquiv X Y').symm g) =
      CategoryTheory.CategoryStruct.comp ((adj.homEquiv X' Y).symm h) k