(* File: Rev_App.v  (last edited on 27/10/2000) (c) Klaus Weich  *)
Require Export In_NGamma.
(*******************************************************************)
(* Decorated nested implications are pairs of a nested implication *)
(* and a counter-model of the premisses.                           *)
Definition decorated_nested_imp := (nimp * kripke_tree)%type.
Definition decorated_nested_imps := list decorated_nested_imp.
Definition DNI_NIL := nil (A:=decorated_nested_imp).
Definition decorated_nested_imp2nimp (x : decorated_nested_imp) :=
match x with
| (x0, _) => x0
end.
Definition decorated_nested_imp2k (x : decorated_nested_imp) :=
match x with
| (_, k) => k
end.
Definition decorated_nested_imp2form (x : decorated_nested_imp) :=
nimp2form (decorated_nested_imp2nimp x).
Fixpoint rev_app (ds : decorated_nested_imps) :
nested_imps -> nested_imps :=
match ds with
| nil => fun ni : nested_imps => ni
| (x, k) :: ds => fun ni : nested_imps => rev_app ds (Decorated x k :: ni)
end.

Lemma rev_app_app :
forall (dni : decorated_nested_imps) (ni : nested_imps),
rev_app dni ni = rev_app dni NNil ++ ni.