∀ {α : Type u_1} {β : Type u_2} [inst : AddCommGroup α] [inst_1 : UniformSpace α] [IsUniformAddGroup α] {f : β → α},
  (CauchySeq fun s => ∑ b ∈ s, f b) ↔ ∀ e ∈ nhds 0, ∃ s, ∀ (t : Set β), Disjoint t ↑s → ∑' (b : ↑t), f ↑b ∈ e