∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (S : Type u_2) [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] [IsLocalization M S], (∀ m ∈ M, IsRegular m) → Function.Injective ⇑(algebraMap R S)