partial commit in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / reverse / path_reverse.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/reverse/path_reverse.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/reverse/path_reverse.etc
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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.