intros work ds ni1 ni2 ai eqv12.
unfold nweight_Sequent in |- *.
apply plus_reg.
apply plus_reg.
generalize (nweight_ai ai); clear work ds ai.
intros n.
rewrite (nweight_eqv_ni ni1 ni2 eqv12).
trivial.
Qed.
(*******************************************************************)

(* Specifications: *)
Lemma nweight_sequent_nimp_left :
forall (a0 a1 : Int) (b : normal_form) (work : nf_list)
(ds : disjs) (ni1 ni2 : nested_imps) (dni1 : decorated_nested_imps)
(ai : atomic_imps) (n : nat),
eqv_ni (rev_app dni1 ni1) ni2 ->
nweight_Sequent work ds (rev_app dni1 (Undecorated (NImp a0 a1 b) :: ni1))
ai < S n -> nweight_Sequent (AImp a1 b :: NAtom a0 :: work) ds ni2 ai < n.