Definition t:= address.Definition eq:= @eq t.Definition lt' (x y:t): bool :=
      (match x, y with (x1,x2),(y1,y2) =>
        if peq x1 y1 then zlt x2 y2 else plt x1 y1
      end).Definition lt x y:= is_true (lt' x y).

Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y.