intros E f.
elim E; unfold map in |- *.
auto.
intros a b Hyp_rec Id_a_b_f.
apply add_add.
auto.
apply Hyp_rec.
apply Id_inclus with (add a b); auto.
Qed.
Definition Id_words (E : Ensf) (f : Word -> Word) :=
forall x : Word, inmonoid E x -> f x = x :>Word.

Lemma Id_words_inv :
forall (E : Ensf) (f : Word -> Word) (x : Word),
inmonoid E x -> Id_words E f -> f x = x :>Word.