intro Hyp.
red in |- *.
intros x inmon; elim inmon; clear inmon.
auto.
intros.
replace (wef (cons e w)) with (cons (f e) (wef w)); auto.
Qed.
Hint Resolve application_imp_application_words.

(* Specifications: *)
Lemma is_mono_f_imp_is_mono_words : is_mono E f -> is_mono_words E wef.
intro Hyp.