∀ {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) {T : Submonoid P} {k : M ≃* P}
  (H : Submonoid.map k.symm.toMonoidHom T = S) (x : M), (f.ofMulEquivOfDom H) (k x) = f x