∀ {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] [inst_2 : CategoryTheory.HasShift C ℤ]
  [inst_3 : CategoryTheory.HasShift D ℤ] (F : CategoryTheory.Functor C D) [inst_4 : F.CommShift ℤ] {X Y : Cᵒᵖ}
  (f : X ⟶ Y) (n : ℤ),
  F.map ((CategoryTheory.shiftFunctor Cᵒᵖ n).map f).unop =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso F.op n).inv.app Y).unop
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor Dᵒᵖ n).map (F.map f.unop).op).unop
        ((CategoryTheory.Functor.commShiftIso F.op n).hom.app X).unop)