intros E F f inclus_F_E Id_E_f.
red in |- *.
intros x inmonoid_F_x.
apply Id_E_f.
apply inmonoid_inclus with F; assumption.
Qed.

Lemma extension_Id :
forall (E : Ensf) (f : Elt -> Elt), Id E f -> Id_words E (Word_ext f).