{α : Type w} →
  [inst : LT α] →
    [inst_1 : LE α] →
      [inst_2 : Std.Roo.HasRcoIntersection α] →
        {motive : Std.Roo.LawfulRcoIntersection α → Sort u} →
          (t : Std.Roo.LawfulRcoIntersection α) →
            ((mem_intersection_iff :
                  ∀ {a : α} {r : Std.Roo α} {s : Std.Rco α},
                    a ∈ Std.Roo.HasRcoIntersection.intersection r s ↔ a ∈ r ∧ a ∈ s) →
                motive ⋯) →
              motive t