∀ {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} (hg : ∀ (y : ↥S), IsAddUnit (g ↑y)),
  f.lift hg =
    { toFun := fun z => g (f.sec z).1 + ↑(-(IsAddUnit.liftRight (g.restrict S) hg) (f.sec z).2), map_zero' := ⋯,
      map_add' := ⋯ }