∀ {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.Functor.commShiftIso (G.comp F) a).hom.app Y)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor D a).map (adj.counit.app Y)) h) =
    CategoryTheory.CategoryStruct.comp (adj.counit.app ((CategoryTheory.shiftFunctor D a).obj Y)) h