∀ {A : Type u_1} [inst : CommRing A] {g : PowerSeries A} {I : Ideal A} (H : g.IsWeierstrassDivisorAt I)
  [inst_1 : IsAdicComplete I A] (f f' : PowerSeries A ⧸ Ideal.span {g}),
  Quotient.lift (fun f => H.mod f) ⋯ (f + f') =
    Quotient.lift (fun f => H.mod f) ⋯ f + Quotient.lift (fun f => H.mod f) ⋯ f'