intros ni1 ni2.
elim ni1; clear ni1.
simpl in |- *; trivial.
intros x ni1 ih.
simpl in |- *.
rewrite ih; trivial.
Qed.

(* Specifications: *)
Lemma nested_imps2nimps_length :
forall ni : nested_imps, length ni = length (nested_imps2nimps ni).