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 getN_obs:
forall f m1 m2 b1 b2,
strong_mem_obs_eq f m1 m2 ->
f b1 = Some b2 ->
forall n ofs,
Mem.range_perm m1 b1 ofs (ofs + Z_of_nat n) Cur Readable ->
list_forall2 (memval_obs_eq f)
(Mem.getN n ofs (m1.(Mem.mem_contents)#b1))
(Mem.getN n ofs (m2.(Mem.mem_contents)#b2)).