intros l0 r r0 b0 Balanced_r0 height_l.
inversion_clear Balanced_r0.
apply Is_Left_Balanced_Avl_Right_Shift.
rewrite H; symmetry  in |- *; assumption.
apply Is_Fully_Balanced_Avl_Right_Shift.
rewrite H; symmetry  in |- *; assumption.
apply Is_Right_Balanced_Avl_Right_Shift.
rewrite H; symmetry  in |- *; assumption.
Qed.

Lemma is_balanced_avl_is_balanced_avl_right_shift_false :
forall (l r : avl_tree) (b : bal),
is_balanced_avl l r b -> is_balanced_avl_right_shift l r b -> False.