intros b c work ds ni ai a forces_bc 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_weak with b; try assumption.
intros forces_c.
apply forces_bc; assumption.
Qed.

(* Specifications: *)
Lemma deco_sound_cons_work_weak2 :
forall (b c d : 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_t k (nf2form b) -> forces_t k (nf2form c) -> forces_t k (nf2form d)) ->
deco_sound (b :: c :: work) ds ni ai a -> deco_sound (d :: work) ds ni ai a.