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 del_shape:
forall x t,
(forall n, is_redblack t Red (S n) -> is_black t -> infrared (del x t) n) /\
(forall n, is_redblack t Black n -> is_red_or_empty t -> is_redblack (del x t) Black n).