Proof with eauto with val_renamings.
intros.
destruct v...
destruct Hvalid as [b' Hf].
specialize (Hid _ _ Hf);
subst...
Qed.

Lemma val_obs_list_id :
forall f vs
(Hvalid: valid_val_list f vs)
(Hf: forall b1 b2, f b1 = Some b2 -> b1 = b2),
val_obs_list f vs vs.