{α : Type u} →
  [t : TopologicalSpace α] →
    {s : Set (Set α)} →
      {motive : TopologicalSpace.IsTopologicalBasis s → Sort u_1} →
        (t_1 : TopologicalSpace.IsTopologicalBasis s) →
          ((exists_subset_inter : ∀ t₁ ∈ s, ∀ t₂ ∈ s, ∀ x ∈ t₁ ∩ t₂, ∃ t₃ ∈ s, x ∈ t₃ ∧ t₃ ⊆ t₁ ∩ t₂) →
              (sUnion_eq : ⋃₀ s = Set.univ) → (eq_generateFrom : t = TopologicalSpace.generateFrom s) → motive ⋯) →
            motive t_1