Definition comp_word (f g : Word -> Word) (x : Word) := f (g x).Definition eg_f_W_W (f g : Word -> Word) := forall x : Word, f x = g x :>Word.

Lemma comp_Word_ext : forall f g : Elt -> Elt, eg_f_W_W (Word_ext (comp f g)) (comp_word (Word_ext f) (Word_ext g)).