{α : Type u_6} →
  {motive : FilterBasis α → Sort u} →
    (t : FilterBasis α) →
      ((sets : Set (Set α)) →
          (nonempty : sets.Nonempty) →
            (inter_sets : ∀ {x y : Set α}, x ∈ sets → y ∈ sets → ∃ z ∈ sets, z ⊆ x ∩ y) →
              motive { sets := sets, nonempty := nonempty, inter_sets := inter_sets }) →
        motive t