(*****************************************************************)


Inductive filter_deco_spec (i : Int) (N : nested_imps) : Set :=
    Filter_Deco_Spec_Intro :
      forall ni1 : nested_imps,
      le_ni N ni1 ->
      (forall (x : nimp) (k : kripke_tree),
       In (Decorated x k) ni1 -> forces_t k (Atom i)) -> 
      filter_deco_spec i N.(*****************************************************************)


Inductive filter_deco_spec (i : Int) (N : nested_imps) : Set :=
    Filter_Deco_Spec_Intro :
      forall ni1 : nested_imps,
      le_ni N ni1 ->
      (forall (x : nimp) (k : kripke_tree),
       In (Decorated x k) ni1 -> forces_t k (Atom i)) -> 
      filter_deco_spec i N.

Lemma filter_deco : forall (i : Int) (ni : nested_imps), filter_deco_spec i ni.