intros.
inversion_clear H.
apply H5; assumption.
Qed.

Lemma equiv_ins_equiv_equiv_ins :
forall (key : Int) (update : B -> B) (init : B) (t0 t1 t2 : avl_tree),
equiv_ins key update init t0 t1 ->
equiv t1 t2 -> equiv_ins key update init t0 t2.