matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.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 "delayed_updating/relocation/tr_minus.ma".
  16 include "ground/relocation/tr_pn.ma".
  17 include "ground/arith/nat_succ.ma".
  18
  19 (* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
  20
  21 (* Constructions with tr_push ***********************************************)
  22
  23 lemma tr_minus_push_succ (f) (n):
  24       (⫯(f-↑n)) = (⫯f)-↑n.
  25 #f #n <tr_minus_cons_inj //
  26 qed.
  27
  28 (* Constructions with tr_next ***********************************************)
  29
  30 lemma tr_minus_next_succ (n) (f:tr_map):
  31       f-n = (↑f)-↑n.
  32 * [| #n ] * #p #f
  33 <tr_minus_cons_inj //
  34 <tr_minus_cons_inj //
  35 qed.