intros gamma work context a minimal0.
unfold minimal in |- *.
intros b k k_is_mon k_forces_gamma in_b.
inversion_clear in_b.
apply k_forces_gamma.
rewrite H.
apply in_gamma_cons_gamma_head.
apply minimal0.
assumption.
apply forces_gamma_cons_gamma_tail with a; assumption.
assumption.
Qed.
(*************************************************************************)

(* Specifications: *)
Lemma minimal_cons_gamma_weak :
forall (gamma : flist) (work : nf_list) (context : flist) (a b : form),
(forall k : kripke_tree,
Is_Monotone_kripke_tree k -> forces_t k b -> forces_t k a) ->
minimal (a :: gamma) work context -> minimal (b :: gamma) work context.