ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / rtmap_tls.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_tls.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_tls.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 "ground/notation/functions/droppreds_2.ma".
+include "ground/relocation/rtmap_pushs.ma".
+include "ground/relocation/rtmap_tl.ma".
+
+(* RELOCATION MAP ***********************************************************)
+
+rec definition tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
+[ O ⇒ f | S m ⇒ ⫱(tls f m) ].
+
+interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
+
+(* Basic properties *********************************************************)
+
+lemma tls_O: ∀f. f = ⫱*[0] f.
+// qed.
+
+lemma tls_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[↑n] f.
+// qed.
+
+lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≡ ⫱*[n] f2).
+#n elim n -n /3 width=1 by tl_eq_repl/
+qed.
+
+(* Advanced properties ******************************************************)
+
+lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[↑n] f.
+#n elim n -n //
+qed.
+
+(* Properties with pushs ****************************************************)
+
+lemma tls_pushs: ∀n,f. f = ⫱*[n] ⫯*[n] f.
+#n elim n -n //
+#n #IH #f <tls_xn //
+qed.