Inductive is_redblack : tree -> color -> nat -> Prop :=
| IsRB_leaf: forall c, is_redblack EE c 0
| IsRB_r: forall tl k tr n,
is_redblack tl Red n ->
is_redblack tr Red n ->
is_redblack (T Red tl k tr) Black n
| IsRB_b: forall c tl k tr n,
is_redblack tl Black n ->
is_redblack tr Black n ->
is_redblack (T Black tl k tr) c (S n).

Lemma is_redblack_toblack:
forall s n, is_redblack s Red n -> is_redblack s Black n.