∀ {α : Type u_1} {ι : Type u_3} [Countable ι] {t : ι → TopologicalSpace α},
  (∃ t₀, T2Space α ∧ ∀ (i : ι), t i ≤ t₀) →
    (∀ (i : ι), ∃ u, CompleteSpace α ∧ (uniformity α).IsCountablyGenerated ∧ u.toTopologicalSpace = t i) →
      ∃ u, CompleteSpace α ∧ (uniformity α).IsCountablyGenerated ∧ u.toTopologicalSpace = ⨅ i, t i