∀ {R : Type u} [inst : CommRing R] [inst_1 : Small.{v, u} R] [IsNoetherianRing R] (n : ℕ) (S : Submonoid R)
  (M : ModuleCat R) [CategoryTheory.HasInjectiveDimensionLE M n],
  CategoryTheory.HasInjectiveDimensionLE (M.localizedModule S) n