intros b c work ds ni ai a k k_is_mon forces_bc k_forces_ngamma.
apply forces_ngamma_cons_work.
apply forces_bc.
apply k_forces_ngamma.
apply in_ngamma_cons_work_head.
apply forces_ngamma_cons_work_tail with b; assumption.
Qed.

(* Specifications: *)
Lemma forces_ngamma_cons_work_weak2 :
forall (b c d : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(k : kripke_tree),
Is_Monotone_kripke_tree k ->
(forces_t k (nf2form b) -> forces_t k (nf2form c) -> forces_t k (nf2form d)) ->
forces_ngamma (b :: c :: work) ds ni ai a k ->
forces_ngamma (d :: work) ds ni ai a k.