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

Lemma modu_ren:
forall f v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2'),
Val.modu v1 v2 = Val.modu v1' v2'.