matita/matita/contribs/lambdadelta/ground/relocation/tr_map.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/element_t_1.ma".
  16 include "ground/relocation/pr_map.ma".
  17 include "ground/arith/pnat.ma".
  18
  19 (* TOTAL RELOCATION MAPS ****************************************************)
  20
  21 definition tr_map: Type[0] ≝ stream pnat.
  22
  23 corec definition tr_inj: tr_map → pr_map.
  24 * *
  25 [ #f @(⫯(tr_inj f))
  26 | #p #f @(↑(tr_inj (p⨮f)))
  27 ]
  28 defined.
  29
  30 interpretation
  31   "injection (total relocation maps)"
  32   'ElementT f = (tr_inj f).
  33
  34 (* Basic constructions ******************************************************)
  35
  36 lemma tr_inj_unfold_unit (f): ⫯𝐭❨f❩ = 𝐭❨𝟏⨮f❩.
  37 #f <(stream_unfold … (𝐭❨𝟏⨮f❩)) in ⊢ (???%); //
  38 qed.
  39
  40 lemma tr_inj_unfold_succ (f): ∀p. ↑𝐭❨p⨮f❩ = 𝐭❨↑p⨮f❩.
  41 #f #p <(stream_unfold … (𝐭❨↑p⨮f❩)) in ⊢ (???%); //
  42 qed.