Definition eq (x y: t) : Prop :=
forall p, L.eq (get p x) (get p y).

Lemma eq_trans: forall x y z, eq x y -> eq y z -> eq x z.
Definition beq (x y: t) : bool :=
match x, y with
| Bot, Bot => true
| Top_except m, Top_except n => PTree.beq L.beq m n
| _, _ => false
end.