intros k d l b avl_t.
apply equiv_del_intro.
intros k0 equal d0 lookup_l.
inversion_clear avl_t.
apply lookup_below_false with k0 l d0.
assumption.
rewrite (equal_eq k0 k equal).
apply is_below_avl_is_below; assumption.
intros k0 data notequal lookup_t.
inversion lookup_t.
rewrite H0 in notequal.
elimtype False.
apply notequal.
apply equal_refl.
assumption.
inversion_clear H5.
intros k0 data notequal lookup_l.
apply Lookup_Left; assumption.
Qed.
(*************************************************************************)

Lemma equiv_del_above :
forall (key : Int) (t0 t : avl_tree) (k0 : Int),
equiv_del key t0 t -> Less k0 key -> is_above t0 k0 -> is_above t k0.