intros X.
simple induction w1.
auto.
intros x w H w2.
replace (Append (cons x w) w2) with (cons x (Append w w2)); auto.
intro.
apply (H w2).
apply inmonoid_cons_inv with x; auto.
Qed.

(* Specifications: *)
Lemma inmonoid_Append :
forall (X : Ensf) (w1 w2 : Word),
inmonoid X w1 -> inmonoid X w2 -> inmonoid X (Append w1 w2).