intros work i j ds ni ai a complete.
unfold deco_sound in |- *.
intros k a0 a1 b in_k.
elim (complete k a0 a1 b in_k); clear complete in_k.
intros k_is_mon k_forces_ngamma k_notforces_i0i1.
apply k_deco_sound_intro; try assumption.
apply forces_ngamma_cons_ds_tail with i j; assumption.
Qed.

Lemma deco_sound_cons_ni_tail :
forall (work : nf_list) (ds : disjs) (x : nested_imp)
(ni : nested_imps) (ai : atomic_imps) (a : atoms),
deco_sound work ds (x :: ni) ai a -> deco_sound work ds ni ai a.