Proof with eauto with val_renamings.
intros.
destruct v1, v2; simpl in *; try discriminate.
destruct (Int.eq i0 Int.zero); try discriminate.
inversion H...
Qed.

Lemma val_obs_modu_id:
forall f v1 v2 v,
Val.modu v1 v2 = Some v ->
val_obs f v v.