∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] (N : Submonoid S) (T : Type u_3) [inst_3 : CommSemiring T] [inst_4 : Algebra R T]
  [inst_5 : Algebra S T] [IsScalarTower R S T] [IsLocalization M S] [IsLocalization N T] (x y : R),
  (algebraMap R T) x = (algebraMap R T) y → ∃ c, ↑c * x = ↑c * y