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


Inductive inf_deco_spec (ni1 ni2 : nested_imps) : Set :=
    Inf_Deco_Spec_Intro :
      forall ni : nested_imps,
      le_ni ni ni1 ->
      eqv_ni ni ni2 ->
      (forall (x : nimp) (k : kripke_tree),
       In (Decorated x k) ni ->
       In (Decorated x k) ni1 \/ In (Decorated x k) ni2) ->
      inf_deco_spec ni1 ni2.(*****************************************************************)


Inductive inf_deco_spec (ni1 ni2 : nested_imps) : Set :=
    Inf_Deco_Spec_Intro :
      forall ni : nested_imps,
      le_ni ni ni1 ->
      eqv_ni ni ni2 ->
      (forall (x : nimp) (k : kripke_tree),
       In (Decorated x k) ni ->
       In (Decorated x k) ni1 \/ In (Decorated x k) ni2) ->
      inf_deco_spec ni1 ni2.

Lemma inf_deco : forall ni1 ni2 : nested_imps, eqv_ni ni1 ni2 -> inf_deco_spec ni1 ni2.