(** * Coq codes *)
(** ** Dependencies *)
Require Export RegExp.Utility.
Require Export RegExp.Definitions.
Require Export RegExp.Boolean.
Require Export RegExp.Concat.
Unset Standard Proposition Elimination Names.
(** ** Lemmas for Star *)
(** ** $ 1 + x x^{\ast} = x $ #1 + x x* = x# *)
(** ** Split [Star] to [list string] *)
(** ** [Star] is morphism *)

Lemma forallb_matches_morphism_s : forall ss r r', r =R= r' ->
forallb (fun s0 => r ~= s0) ss = forallb (fun s0 => r' ~= s0) ss.