∀ {R : Type u_1} [inst : Semiring R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] {R₀ : Type u_2}
  [inst_2 : CommSemiring R₀] [inst_3 : Algebra R₀ R] (r : R₀) (x : OreLocalization S R),
  (OreLocalization.numeratorRingHom.comp (algebraMap R₀ R)) r * x =
    x * (OreLocalization.numeratorRingHom.comp (algebraMap R₀ R)) r