intros key T T'.
elim T; clear T; intros t avl_t.
elim T'; clear T'; intros t' avl_t'.
simpl in |- *.
intros reg_t equiv_del.
apply regular_equiv_del with key t; assumption.
Qed.

(* Specifications: *)
Lemma regular_EQUIV_INS :
forall (key : Int) (data : A) (T T' : AVL (list A)),
REGULAR T -> EQUIV_INS (list A) key (cons data) nil T T' -> REGULAR T'.