intros.
inversion H.
apply H2 with (k := k) (d := d); assumption.
Qed.

Lemma inv_equiv_del_notequal0 :
forall (key : Int) (t0 t : avl_tree) (k : Int) (d : B),
equiv_del key t0 t -> ~ Equal k key -> lookup k t0 d -> lookup k t d.