Proof using.
intros c; apply restrict_code_encode_incl; auto with datatypes.
Qed.

(* Specifications: *)
(* The restriction does not change the unique prefix property if the message is in the alphabet *)
Theorem restrict_unique_prefix :
forall c : code A,
not_null c ->
in_alphabet m c -> unique_prefix c -> unique_prefix (restrict_code m c).