Proof with eauto with val_renamings.
intros v v' v'' f f' f'' Hval'' Hval' Hf.
inversion Hval'; subst; inversion Hval''; subst...
Qed.

(** Two values that are equal are related by the id injection on a valid memory*)
Lemma val_obs_id:
forall f v
(Hvalid: valid_val f v)
(Hid: forall b b', f b = Some b' -> b = b'),
val_obs f v v.