∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) (A : Type u_2) [inst_1 : CommSemiring A]
  [inst_2 : Algebra R A] [inst_3 : IsLocalization S A] (x : R) (s : ↥S),
  IsLocalization.mk' A x s = IsLocalizedModule.mk' (Algebra.linearMap R A) x s