(** ** 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_xs_x : forall (xs:list string)(x:string),
concat_list_string (xs ++ x::nil) = ((concat_list_string xs) ++ x)%string.