(* File: Minimal.v  (last edited on 27/10/2000) (c) Klaus Weich  *)
Require Export Forces_Gamma.
Require Export Derivable_Tools.
Definition minimal (gamma : flist) (work : nf_list)
(context : flist) :=
forall (a : form) (k : kripke_tree),
Is_Monotone_kripke_tree k ->
forces_gamma gamma work k -> In a context -> forces_t k a.

Lemma minimal_derivable_forces :
forall (gamma : flist) (work : nf_list) (context : flist) (k : kripke_tree),
Is_Monotone_kripke_tree k ->
forces_gamma gamma work k ->
minimal gamma work context ->
forall a : form, Derivable context a -> forces_t k a.