intros ni1 ni2 work ds ai a le12 complete.
unfold deco_sound in |- *.
intros k i0 i1 j in_k.
elim complete with k i0 i1 j.
intros k_is_mon k_forces_ngamma k_notforces_i0i1.
apply k_deco_sound_intro; try assumption.
apply forces_ngamma_eqv with ni1.
apply ge_eqv; assumption.
assumption.
apply in_k_le with ni2; assumption.
Qed.
(*********************************************************************)

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