∀ {α : Type u_1} {f : ℤ → α} [inst : CommGroup α] [inst_1 : TopologicalSpace α] [ContinuousMul α] {a : α},
  HasProd f a (SummationFilter.symmetricIcc ℤ) →
    Filter.Tendsto (fun N => (f ↑N)⁻¹) Filter.atTop (nhds 1) → HasProd f a (SummationFilter.symmetricIco ℤ)