∀ (𝕜 : Type u_3) (V : Type u_4) [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup V]
  [inst_2 : NormedSpace 𝕜 V] [TopologicalSpace.SeparableSpace V],
  ∃ gs, (∀ (n : ℕ), Continuous (gs n)) ∧ ∀ ⦃x y : WeakDual 𝕜 V⦄, x ≠ y → ∃ n, gs n x ≠ gs n y