∀ {R : Type u_1} {V : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup V] [inst_2 : TopologicalSpace V]
  [inst_3 : TopologicalSpace R] [inst_4 : Module R V], (∀ (x : V), x ≠ 0 → ∃ f, f x ≠ 0) → SeparatingDual R V