∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N] {P : Type u_3}
  [inst_2 : CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {Q : Type u_4} [inst_3 : CommMonoid Q],
  Function.Surjective ⇑g → ∀ (k : (Submonoid.map g S).LocalizationMap Q), Function.Surjective ⇑(f.map ⋯ k)