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 concat_avl : forall m1 m2, avl m1 -> avl m2 -> avl (concat m1 m2).