Ltac avl_nn_hyp H :=
     let nz := fresh "nz" in assert (nz := height_non_negative H).Ltac avl_nn h :=
  let t := type of h in
  match type of t with
   | Prop => avl_nn_hyp h
   | _ => match goal with H : avl h |- _ => avl_nn_hyp H end
  end.(* Repeat the previous tactic.
   Drawback: need to clear the [avl _] hyps ... Thank you Ltac *)

Ltac avl_nns :=
  match goal with
     | H:avl _ |- _ => avl_nn_hyp H; clear H; avl_nns
     | _ => idtac
  end.

Lemma empty_avl : avl (empty elt).