(** * 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] *)

Lemma divide_Star_left : forall s r, (Star r) ~== s -> s <> ""%string ->
{s':string & {s'':string | s = (s' ++ s'')%string /\ s'' <> ""%string /\
(Star r) ~== s' /\ r ~== s''}}.