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

Lemma forallb_list_xs_x : forall A (f:A -> bool)(xs:list A)(x:A),
forallb f xs = true -> f x = true -> forallb f (xs ++ x::nil)%list = true.