(** * Coq codes *)
(** ** Dependencies *)
Require Export RegExp.Utility.
Require Export RegExp.Definitions.
(** ** [Empty] *)
(** [Empty] corresponds to 0 in Kleene algebra. *)

(* Specifications: *)
Lemma Empty_false : forall s, Empty ~!= s.
(** ** [Eps] *)
(** [Eps] corresponds to 1 in Kleene algebra. *)
Lemma Eps_true : Eps ~== EmptyString.
Lemma Eps_false : forall s, s <> ""%string -> Eps ~!= s.
Add Parametric Morphism : Or with
signature re_eq ==> re_eq ==> re_eq as Or_morphism.