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.

(* Specifications: *)
Lemma beq_correct: forall x y, beq x y = true -> eq x y.
Lemma beq_correct: forall x y, beq x y = true -> eq x y.