{α : Type u_1} →
  {S : Set (Set α)} →
    {motive : FiniteInter S → Sort u} →
      ((univ_mem : Set.univ ∈ S) → (inter_mem : ∀ ⦃s : Set α⦄, s ∈ S → ∀ ⦃t : Set α⦄, t ∈ S → s ∩ t ∈ S) → motive ⋯) →
        (t : FiniteInter S) → motive t