(** * Coq codes *)
(** ** Dependencies *)
Require Export RegExp.Utility.
Require Export RegExp.Definitions.
Require Export RegExp.Boolean.
(** ** [Cat] is morphism *)
Add Parametric Morphism : Cat with
signature re_eq ==> re_eq ==> re_eq as Cat_mor.
(** ** [Empty] *)
(** [Empty] corresponds to 0 in Kleene algebra. *)

Lemma Cat_right_zero_s : forall s r, (r ++ Empty) ~= s = false.