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

(* Specifications: *)
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.
Lemma memval_obs_eq_id:
forall f mv
(Hvalid: valid_memval f mv)
(Hid: forall b b', f b = Some b' -> b = b'),
memval_obs_eq f mv mv.
Lemma ren_cmp_bool:
forall f v v' v0 cmp,
val_obs f v v' ->
Val.cmp_bool cmp v v0 = Val.cmp_bool cmp v' v0.
Lemma val_obs_hiword:
forall f v v',
val_obs f v v' ->
val_obs f (Val.hiword v) (Val.hiword v').