(** ** Lemmas for list *)
Definition concat_list_string(xs:list string) :=
fold_right (fun s s' : string => (s ++ s')%string) ""%string xs.

Lemma concat_list_string_x_xs : forall (x:string)(xs:list string),
concat_list_string (x :: xs) = (x ++ (concat_list_string xs))%string.