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