intros i bs work ds ni ai ai' lookup reg_ai lin_del.
unfold nweight_Sequent in |- *.
generalize (nweight_ds ds); clear ds; intro ds.
generalize (nweight_ni ni); clear ni; intro ni.
rewrite (nweight_work_app bs work).
generalize (nweight_work work); clear work; intro W.
rewrite (plus_comm (nweight_work bs) W).
rewrite
(plus_assoc_reverse W (nweight_work bs) (ds + (ni + nweight_ai ai')))
.
apply plus_lt_compat_l.
rewrite (plus_permute (nweight_work bs) ds (ni + nweight_ai ai')).
apply plus_lt_compat_l.
rewrite (plus_permute (nweight_work bs) ni (nweight_ai ai')).
apply plus_lt_compat_l.
apply nweight_ai_del with i; assumption.
Qed.
(*************************************************************************)

Lemma nweight_sequent_eqv :
forall (work : nf_list) (ds : disjs) (ni1 ni2 : nested_imps)
(ai : atomic_imps),
eqv_ni ni1 ni2 ->
nweight_Sequent work ds ni1 ai = nweight_Sequent work ds ni2 ai.