intros key t0 t1 t2 equiv_del0 equiv0.
inversion_clear equiv_del0.
inversion_clear equiv0.
apply equiv_del_intro.
intros k equal data lookup_t2.
apply H with k data.
assumption.
apply H3; assumption.
intros k data notequal lookup_t0.
apply H2.
apply H0; assumption.
intros k data notequal lookup_t2.
apply H1.
assumption.
apply H3; assumption.
Qed.
(*****************************************************************)

Lemma equiv_del_semi_leave :
forall (k : Int) (d : B) (l : avl_tree) (b : bal),
is_avl (Avl_Node k d l Avl_Nil b) ->
equiv_del k (Avl_Node k d l Avl_Nil b) l.