Proof with eauto with val_renamings.
intros.
destruct v1; inversion Hval_obs; subst;
simpl...
Qed.

Lemma val_obs_sub:
forall f v1 v2 v1' v2'
(Hinjective: forall b1 b1' b2,
f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1')
(Hval_obs': val_obs f v1' v2')
(Hval_obs: val_obs f v1 v2),
val_obs f (Val.sub v1 v1') (Val.sub v2 v2').