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 proj_value_obs:
forall f q vl1 vl2,
(forall b1 b1' b2 : block, f b1 = Some b2 -> f b1' = Some b2 -> b1 = b1') ->
Coqlib.list_forall2 (memval_obs_eq f) vl1 vl2 ->
val_obs f (proj_value q vl1) (proj_value q vl2).