simple induction w.
auto.
intros x w0 H H0.
cut (dans x X /\ Inmonoid X w0); auto.
intro H1; elim H1; clear H1.
auto.
Qed.
Hint Resolve I_i.

(* Specifications: *)
Lemma inmonoid_cons_inv :
forall (X : Ensf) (w : Word) (a : Elt),
inmonoid X (cons a w) -> inmonoid X w.