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).