intros b c d work ds ni ai a forces_bcd complete.
unfold deco_sound in |- *.
intros k i0 i1 j in_k.
elim (complete k i0 i1 j in_k); clear complete in_k.
intros k_is_mon k_forces_ngamma k_nonforces.
apply k_deco_sound_intro; try assumption.
apply forces_ngamma_cons_work_weak2 with b c; try assumption.
intros forces_b forces_c.
apply forces_bcd; assumption.
Qed.

Lemma deco_sound_cons_work_strength :
forall (b c : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms),
(forall k : kripke_tree,
Is_Monotone_kripke_tree k ->
forces_ngamma (b :: work) ds ni ai a k -> forces_t k (nf2form c)) ->
deco_sound (b :: work) ds ni ai a -> deco_sound (c :: work) ds ni ai a.