Ltac omega_bal := match goal with
  | H:avl ?l, H':avl ?r |- context [ bal ?l ?x ?e ?r ] =>
     generalize (bal_height_1 x e H H') (bal_height_2 x e H H');
     omega_max
  end.

Lemma add_avl_1 : forall m x e, avl m -> avl (add x e m) /\ 0 <= height (add x e m) - height m <= 1.