{α : Type u_1} →
  {ι : Sort u_4} →
    {p : ι → Prop} →
      {s : ι → Set α} →
        {motive : Filter.IsBasis p s → Sort u} →
          (t : Filter.IsBasis p s) →
            ((nonempty : ∃ i, p i) → (inter : ∀ {i j : ι}, p i → p j → ∃ k, p k ∧ s k ⊆ s i ∩ s j) → motive ⋯) →
              motive t