intros u v H.
elim H; clear H u v.
intros u v A dans_A.
replace (wef (cons A v)) with (cons (f A) (wef v)).
replace (wef (Append u v)) with (Append (wef u) (wef v)).
auto.
apply sym_equal; unfold wef in |- *; apply wef_append; auto.
auto.
intros.
replace (wef (cons x u)) with (cons (f x) (wef u)).
replace (wef (cons x v)) with (cons (f x) (wef v)); auto.
auto.
Qed.
Hint Resolve Derive_image.

Lemma Derivestar_image :
forall u v : Word, Derivestar R1 u v -> Derivestar Rim (wef u) (wef v).