intros key t0 t k0 equiv_t0 greater below_t0.
apply lookup_greater_above.
intros k d lookup_t.
elim (equal_dec k key).
intro equal.
apply (less_equal_less k0 key k).
assumption.
apply equal_sym; assumption.
intro notequal.
apply (lookup_above_greater k t0 d).
inversion_clear equiv_t0.
apply H1; assumption.
assumption.
Qed.

Lemma equiv_del_right :
forall (key k0 : Int) (d0 : B) (l0 r0 : avl_tree)
(b0 : bal) (r : avl_tree) (b : bal),
is_avl (Avl_Node k0 d0 l0 r0 b0) ->
Less k0 key ->
equiv_del key r0 r ->
equiv_del key (Avl_Node k0 d0 l0 r0 b0) (Avl_Node k0 d0 l0 r b).