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

Lemma forallb_list_x_xs : forall A (f:A -> bool)(x:A)(xs:list A),
f x = true -> forallb f xs = true -> forallb f (x::xs) = true.