intros dni; elim dni; clear dni.
intros; trivial.
intros x; case x; clear x.
intros x k dni ih ni.
simpl in |- *.
apply (ih (Decorated x k :: ni)).
Qed.

(* Specifications: *)
Lemma le_ks_le_count_undecs :
forall (ni1 : nested_imps) (dni1 : decorated_nested_imps)
(ni2 : nested_imps) (dni2 : decorated_nested_imps),
le_ni (rev_app dni1 ni1) (rev_app dni2 ni2) ->
count_undecs ni1 <= count_undecs ni2.