∀ {X : Type u_1} [inst : TopologicalSpace X],
  ∀ s ∈ {P | P ⊆ constructibleTopologySubbasis X ∧ (∀ Q ⊆ P, Q.Finite → (⋂₀ Q).Nonempty) ∧ ⋂₀ P = ∅},
    ∀ c ⊆ {P | P ⊆ constructibleTopologySubbasis X ∧ (∀ Q ⊆ P, Q.Finite → (⋂₀ Q).Nonempty) ∧ ⋂₀ P = ∅},
      ∀ x ∈ c, ⋂₀ ⋃₀ c = ∅