∀ {R : Type u} [inst : CommSemiring R] {S : Submonoid R} (T : Type u_1) [inst_1 : CommSemiring T] [inst_2 : Algebra R T]
  [inst_3 : IsLocalization S T] {A : Type u_2} [inst_4 : Semiring A] [inst_5 : Algebra R A] (a : R) (s : ↥S),
  (algebraMap T (LocalizedModule S A)) (IsLocalization.mk' T a s) = LocalizedModule.mk ((algebraMap R A) a) s