(* File: Le_Ks.v  (last edited on 27/10/2000) (c) Klaus Weich  *)
Require Export Rev_App.
(*****************************************************************)
Inductive le_ni : nested_imps -> nested_imps -> Prop :=
| Le_NI_Nil : le_ni NNil NNil
| Le_NI_Cons_NN :
forall (x : nimp) (ni1 ni2 : nested_imps),
le_ni ni1 ni2 -> le_ni (Undecorated x :: ni1) (Undecorated x :: ni2)
| Le_NI_Cons_DN :
forall (x : nimp) (k : kripke_tree) (ni1 ni2 : nested_imps),
le_ni ni1 ni2 -> le_ni (Decorated x k :: ni1) (Undecorated x :: ni2)
| Le_NI_Cons_DD :
forall (x : nimp) (k : kripke_tree) (ni1 ni2 : nested_imps),
le_ni ni1 ni2 -> le_ni (Decorated x k :: ni1) (Decorated x k :: ni2).

Lemma in_k_le :
forall (ni1 ni2 : nested_imps) (x : nimp) (k : kripke_tree),
le_ni ni1 ni2 -> In (Decorated x k) ni2 -> In (Decorated x k) ni1.