repeat rewrite PTree.fold_spec.
simpl in *. repeat rewrite <- fold_left_rev_right.
induction (rev (PTree.elements t2)).
+ reflexivity.
+ simpl. rewrite IHl. auto.
Qed.

Lemma LocalD_app_eq :
forall t1 t2 q,
LocalD t1 t2 q = LocalD_app t1 t2 q.