elim is_iso_f; intros.
split; auto.
Qed.
Let invf' := inv E F f.
Let weinvf := Word_ext invf'.
Let weinvf_wef := comp_word weinvf wef.

Lemma is_iso_f_imp_Id_words_weinvf_wef :
is_iso E F f -> Id_words E weinvf_wef.