matita/matita/contribs/lambdadelta/ground/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/notation/functions/droppreds_2.ma".
  16 include "ground/relocation/rtmap_pushs.ma".
  17 include "ground/relocation/rtmap_tl.ma".
  18
  19 (* RELOCATION MAP ***********************************************************)
  20
  21 rec definition tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
  22 [ O ⇒ f | S m ⇒ ⫱(tls f m) ].
  23
  24 interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma tls_O: ∀f. f = ⫱*[0] f.
  29 // qed.
  30
  31 lemma tls_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[↑n] f.
  32 // qed.
  33
  34 lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≡ ⫱*[n] f2).
  35 #n elim n -n /3 width=1 by tl_eq_repl/
  36 qed.
  37
  38 (* Advanced properties ******************************************************)
  39
  40 lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[↑n] f.
  41 #n elim n -n //
  42 qed.
  43
  44 (* Properties with pushs ****************************************************)
  45
  46 lemma tls_pushs: ∀n,f. f = ⫱*[n] ⫯*[n] f.
  47 #n elim n -n //
  48 #n #IH #f <tls_xn //
  49 qed.