∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : CommMonoid α] {f : ι → β → α} {g : β → α}
  [inst_1 : UniformSpace α], HasProdUniformly f g ↔ TendstoUniformly (fun x1 x2 => ∏ i ∈ x1, f i x2) g Filter.atTop