∀ {M : Type u_2} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_1} [inst_1 : AddCommMonoid N] {P : Type u_3}
  [inst_2 : AddCommMonoid P] (f : S.LocalizationMap N) {T : AddSubmonoid P} {k : P ≃+ M}
  (H : AddSubmonoid.map k.toAddMonoidHom T = S) (y : ↥T) (motive : IsAddUnit (f ↑⟨k ↑y, ⋯⟩) → Prop)
  (x : IsAddUnit (f ↑⟨k ↑y, ⋯⟩)), (∀ (z : AddUnits N) (hz : ↑z = f ↑⟨k ↑y, ⋯⟩), motive ⋯) → motive x