Proof with eauto with val_renamings.
intros.
destruct v1, v2; simpl in *; try discriminate.
match goal with
| [H: match ?Expr with _ => _ end = _ |- _] =>
destruct Expr
end; try discriminate.
inversion H...
Qed.

(* Specifications: *)
Lemma val_obs_mods_id:
forall f v1 v2 v,
Val.mods v1 v2 = Some v ->
val_obs f v v.
Lemma divlu_ren:
forall f v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2'),
Val.divlu v1 v2 = Val.divlu v1' v2'.
Lemma modlu_ren:
forall f v1 v2 v1' v2'
(Hval_obs: val_obs f v1 v1')
(Hval_obs': val_obs f v2 v2'),
Val.modlu v1 v2 = Val.modlu v1' v2'.
Lemma val_obs_divlu_id:
forall f v1 v2 v,
Val.divlu v1 v2 = Some v ->
val_obs f v v.
Lemma val_obs_modls_id:
forall f v1 v2 v,
Val.modls v1 v2 = Some v ->
val_obs f v v.
Lemma val_obs_of_bool:
forall f b,
val_obs f (Val.of_bool b) (Val.of_bool b).