∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
  [inst_3 : Ring β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] {f : CauSeq β abv} (g : CauSeq β abv),
  f.LimZero → (f * g).LimZero