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

(* Specifications: *)
Lemma Id_words_inv : forall (E : Ensf) (f : Word -> Word) (x : Word), inmonoid E x -> Id_words E f -> f x = x :>Word.
Lemma Id_words_inclus : forall (E F : Ensf) (f : Word -> Word), inclus F E -> Id_words E f -> Id_words F f.
Lemma extension_Id : forall (E : Ensf) (f : Elt -> Elt), Id E f -> Id_words E (Word_ext f).