intros; trivial.
intros k d l ih_l r ih_r b.
simpl in |- *; intro u0;  discriminate u0.
Qed.
(*********************************************************)
(*		Definition is_balanced		  	 *)
Inductive is_balanced (l r : avl_tree) : bal -> Prop :=
| Is_Left_Balanced :
height l = S (height r) -> is_balanced l r Left_Balanced
| Is_Fully_Balanced : height l = height r -> is_balanced l r Balanced
| Is_Right_Balanced :
S (height l) = height r -> is_balanced l r Right_Balanced.

Lemma inv_left_balanced :
forall l r : avl_tree,
is_balanced l r Left_Balanced -> height l = S (height r).