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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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 definition tls (f:rtmap) (n:nat) ≝ tl^n f.
  22
  23 interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
  24
  25 (* Basic properties *********************************************************)
  26
  27 lemma tls_O: ∀f. f = ⫱*[𝟎] f.
  28 // qed.
  29
  30 lemma tls_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[↑n] f.
  31 #f #n @(niter_succ … tl)
  32 qed.
  33
  34 lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≡ ⫱*[n] f2).
  35 #n @(nat_ind_succ … n) -n /3 width=1 by tl_eq_repl/
  36 qed.
  37
  38 (* Advanced properties ******************************************************)
  39
  40 lemma tls_swap (n) (f): ⫱ ⫱*[n] f = ⫱*[n] ⫱f.
  41 #f #n @(niter_appl … tl)
  42 qed.
  43
  44 lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[↑n] f.
  45 // qed.
  46
  47 (* Properties with pushs ****************************************************)
  48
  49 lemma tls_pushs: ∀n,f. f = ⫱*[n] ⫯*[n] f.
  50 #n @(nat_ind_succ … n) -n //
  51 #n #IH #f <tls_xn <pushs_S <tl_push_rew //
  52 qed.