Proof with eauto with renamings id_renamings val_renamings.
intros.
constructor; constructor;
eauto with id_renamings; unfold id_ren; intros;
repeat match goal with
| [H: context[valid_block_dec ?M ?B] |- _] =>
destruct (valid_block_dec M B); simpl in *
| [H: _ = Some _ |- _] => inv H; clear H
end; auto.
now apply po_refl.
destruct (ZMap.get ofs (Mem.mem_contents m) # b2) eqn:Hget;
constructor.
destruct v0; constructor.
specialize (H _ v _ _ Hget).
simpl in H.
destruct (valid_block_dec m b); simpl; tauto.
Qed.

Lemma check_value_obs:
forall f n vl vl' v v' q
(Hf: forall b1 b1' b2, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1'),
Coqlib.list_forall2 (memval_obs_eq f) vl vl' ->
val_obs f v v' ->
check_value n v q vl = check_value n v' q vl'.