partial commit in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / path_reverse.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_reverse.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_reverse.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/functions/nec_r_1.ma".
-
-(* REVERSE FOR PATH *********************************************************)
-
-rec definition reverse (p) on p: path ≝
-match p with
-[ list_empty     ⇒ 𝐞
-| list_lcons l q ⇒ (reverse q)◖l
-].
-
-interpretation
-  "reverse (path)"
-  'NEcR p = (reverse p).
-
-(* Basic constructions ******************************************************)
-
-lemma reverse_empty: 𝐞 = 𝐞ᴿ.
-// qed.
-
-lemma reverse_lcons (p) (l): pᴿ◖l = (l◗p)ᴿ.
-// qed.
-
-(* Main constructions *******************************************************)
-
-theorem reverse_append (p1) (p2):
-        (p2ᴿ)●(p1ᴿ) = (p1●p2)ᴿ.
-#p1 elim p1 -p1 //
-#l1 #p1 #IH #p2
-<list_append_lcons_sn <reverse_lcons <reverse_lcons //
-qed.
-
-(* Constructions with list_rcons ********************************************)
-
-lemma reverse_rcons (p) (l):
-      l◗(pᴿ) = (p◖l)ᴿ.
-#p #l
-<reverse_append //
-qed.
-
-(* Main constructions *******************************************************)
-
-theorem reverse_reverse (p):
-        p = pᴿᴿ.
-#p elim p -p //
-#l #p #IH
-<reverse_lcons <reverse_rcons //
-qed.