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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                                 Marks.v                                  *)
(*                                                                          *)
(*                                Gerard Huet                               *)
(*                                                                          *)
(* Developed in V5.8  January 1993                                          *)
(* Ported    to V5.10 January 1995                                          *)
(****************************************************************************)
(* Translation from terms to redexes *)
Fixpoint mark (e : lambda) : redexes :=
match e with
| Ref n => Var n
| Abs M => Fun (mark M)
| App M N => Ap false (mark M) (mark N)
end.
(* Reverse translation : erasing the marks *)
Fixpoint unmark (e : redexes) : lambda :=
match e with
| Var n => Ref n
| Fun U => Abs (unmark U)
| Ap b U V => App (unmark U) (unmark V)
end.

Lemma inverse : forall M : lambda, M = unmark (mark M).