Definition is_red_or_empty t :=
  match t with T Black _ _ _ => False | _ => True end.Definition is_black t :=
  match t with T Black _ _ _ => True | _ => False end.

Lemma interp_balance': forall tl k tr x, interp (balance' tl k tr) x <-> K.eq x k \/ interp tl x \/ interp tr x.