matita/matita/contribs/lambdadelta/ground/relocation/tr_pap_eq.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/lib/stream_eq.ma".
  16 include "ground/relocation/tr_pap.ma".
  17
  18 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
  19
  20 (* Main constructions with stream_eq ****************************************)
  21
  22 (* Note: a better statement would be: tr_eq_repl … (λf1,f2. f1@❨i❩ = f2@❨i❩) *)
  23 (*** apply_eq_repl *)
  24 theorem apply_eq_repl (i):
  25         ∀f1,f2. f1 ≗ f2 → f1@❨i❩ = f2@❨i❩.
  26 #i elim i -i [2: #i #IH ] * #p1 #f1 * #p2 #f2 #H
  27 elim (stream_eq_inv_cons_bi … H) -H [1,8: |*: // ] #Hp #Hf //
  28 <tr_pap_succ <tr_pap_succ /3 width=1 by eq_f2/
  29 qed.
  30
  31 (* Main inversions with stream_eq *******************************************)
  32
  33 corec theorem nstream_eq_inv_ext:
  34               ∀f1,f2. (∀i. f1@❨i❩ = f2@❨i❩) → f1 ≗ f2.
  35 * #p1 #f1 * #p2 #f2 #Hf @stream_eq_cons
  36 [ @(Hf (𝟏))
  37 | @nstream_eq_inv_ext -nstream_eq_inv_ext #i
  38   lapply (Hf (𝟏)) <tr_pap_unit <tr_pap_unit #H destruct
  39   lapply (Hf (↑i)) <tr_pap_succ <tr_pap_succ #H
  40   /3 width=2 by eq_inv_pplus_bi_dx, eq_inv_psucc_bi/
  41 ]
  42 qed-.