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

Lemma val_obs_shl:
forall f v1 v2 v1' v2'
(Hval_obs': val_obs f v1' v2')
(Hval_obs: val_obs f v1 v2),
val_obs f (Val.shl v1 v1') (Val.shl v2 v2').