∀ {C : Type u_6} {D : Type u_2} {H : Type u_4} [inst : CategoryTheory.Category.{u_5, u_6} C]
  [inst_1 : CategoryTheory.Category.{u_3, u_2} D] [inst_2 : CategoryTheory.Category.{u_1, u_4} H]
  (LF' LF : CategoryTheory.Functor D H) {F F' : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α' : L.comp LF' ⟶ F') (α : L.comp LF ⟶ F) (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
  [inst_4 : LF.IsLeftDerivedFunctor α W] [inst_5 : LF'.IsLeftDerivedFunctor α' W] (τ : F' ≅ F),
  CategoryTheory.CategoryStruct.comp (LF'.leftDerivedNatTrans LF α' α W τ.hom)
      (LF.leftDerivedNatTrans LF' α α' W τ.inv) =
    CategoryTheory.CategoryStruct.id LF'