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 merge_avl_1 : forall m1 m2, avl m1 -> avl m2 -> -(2) <= height m1 - height m2 <= 2 -> avl (merge m1 m2) /\ 0<= height (merge m1 m2) - max (height m1) (height m2) <=1.