∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) {A : Type u_3} [inst_2 : AddMonoid A] [inst_3 : CategoryTheory.HasShift C A]
  [inst_4 : CategoryTheory.HasShift D A] [inst_5 : F.CommShift A] [inst_6 : G.CommShift A] [adj.CommShift A] (a : A)
  (Y : D) {Z : D} (h : (CategoryTheory.shiftFunctor D a).obj Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D a).map (adj.counit.app Y)) h =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso F a).inv.app (G.obj Y))
      (CategoryTheory.CategoryStruct.comp (F.map ((CategoryTheory.Functor.commShiftIso G a).inv.app Y))
        (CategoryTheory.CategoryStruct.comp (adj.counit.app ((CategoryTheory.shiftFunctor D a).obj Y)) h))