∀ {α : Type u_1} {β : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : UniformSpace R] [IsUniformAddGroup R]
  [NonarchimedeanRing R] {f : α → R} {g : β → R} {a b : R},
  HasSum f a → HasSum g b → HasSum (fun i => f i.1 * g i.2) (a * b)