∀ {α : Type w} [inst : LT α] [inst_1 : LE α] [inst_2 : Std.Rci.HasRcoIntersection α],
  (∀ {a : α} {r : Std.Rci α} {s : Std.Rco α}, a ∈ Std.Rci.HasRcoIntersection.intersection r s ↔ a ∈ r ∧ a ∈ s) →
    Std.Rci.LawfulRcoIntersection α