intros; trivial.
intros k d l ih_l r ih_r b.
elim b; simpl in |- *; intro u0;  discriminate u0.
Qed.
(*********************************************************)
(*		Definition is_balanced		  	 *)
Inductive is_balanced_avl (l r : avl_tree) : bal -> Prop :=
| Is_Left_Balanced_Avl :
height_avl l = S (height_avl r) -> is_balanced_avl l r Left_Balanced
| Is_Fully_Balanced_Avl :
height_avl l = height_avl r -> is_balanced_avl l r Balanced
| Is_Right_Balanced_Avl :
S (height_avl l) = height_avl r -> is_balanced_avl l r Right_Balanced.

Lemma inv_left_balanced_avl :
forall l r : avl_tree,
is_balanced_avl l r Left_Balanced -> height_avl l = S (height_avl r).