Definition tree_eq (m1 m2: PTree.t L.t) : Prop :=
  forall i, opt_eq (PTree.get i m1) (PTree.get i m2).

Lemma tree_eq_trans: forall m1 m2 m3, tree_eq m1 m2 -> tree_eq m2 m3 -> tree_eq m1 m3.