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.

(* Specifications: *)
Lemma val_obs_modu_id:
forall f v1 v2 v,
Val.modu v1 v2 = Some v ->
val_obs f v v.
Lemma divs_ren:
forall f v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2'),
Val.divs v1 v2 = Val.divs v1' v2'.
Lemma mods_ren:
forall f v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2'),
Val.mods v1 v2 = Val.mods v1' v2'.
Lemma val_obs_divs_id:
forall f v1 v2 v,
Val.divs v1 v2 = Some v ->
val_obs f v v.