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