matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_tls.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/notation/functions/droppreds_2.ma".
  16 include "ground_2/relocation/rtmap_tl.ma".
  17
  18 (* RELOCATION MAP ***********************************************************)
  19
  20 rec definition tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
  21 [ O ⇒ f | S m ⇒ ⫱(tls f m) ].
  22
  23 interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
  24
  25 (* Basic properties *********************************************************)
  26
  27 lemma tls_rew_O: ∀f. f = ⫱*[0] f.
  28 // qed.
  29
  30 lemma tls_rew_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[⫯n] f.
  31 // qed.
  32
  33 lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≗ ⫱*[n] f2).
  34 #n elim n -n /3 width=1 by tl_eq_repl/
  35 qed.
  36
  37 (* Advancedd properties *****************************************************)
  38
  39 lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[⫯n] f.
  40 #n elim n -n //
  41 qed.