(* File: niMinimal.v  (last edited on 27/10/2000) (c) Klaus Weich  *)
Require Export Forces_NGamma.
Require Export Derivable_Tools.
Definition nminimal (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (a : atoms) (context : flist) :=
forall (c : form) (k : kripke_tree),
Is_Monotone_kripke_tree k ->
forces_ngamma work ds ni ai a k -> In c context -> forces_t k c.
(*********************************************************************)

Lemma nminimal_derivable_forces :
forall (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (a : atoms) (context : flist)
(k : kripke_tree),
Is_Monotone_kripke_tree k ->
forces_ngamma work ds ni ai a k ->
nminimal work ds ni ai a context ->
forall c : form, Derivable context c -> forces_t k c.