∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (S : Type u_2) [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] [inst_3 : IsLocalization M S] (x₁ x₂ : R) (y₁ y₂ : ↥M),
  IsLocalization.mk' S x₁ y₁ * IsLocalization.mk' S x₂ y₂ = IsLocalization.mk' S (x₁ * x₂) (y₁ * y₂)