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.
(** * Insertion *)

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