∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommGroup α] [IsUniformAddGroup α] {f : β → α},
  (CauchySeq fun s => ∑ b ∈ s, f b) ↔ ∀ e ∈ nhds 0, ∃ s, ∀ (t : Finset β), Disjoint t s → ∑ b ∈ t, f b ∈ e