matita/matita/contribs/lambdadelta/ground/relocation/tr_compose_pushs.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/relocation/tr_pushs.ma".
  16 include "ground/relocation/tr_compose_pn.ma".
  17
  18 (* COMPOSITION FOR TOTAL RELOCATION MAPS ************************************)
  19
  20 (* Constructions with tr_pushs **********************************************)
  21
  22 lemma tr_compose_pushs_bi (n) (f2) (f1):
  23       (⫯*[n](f2∘f1)) = (⫯*[n]f2)∘(⫯*[n]f1).
  24 #n @(nat_ind_succ … n) -n //
  25 #n #IH #f1 #f2
  26 <tr_pushs_succ <tr_pushs_succ <tr_pushs_succ
  27 <tr_compose_push_bi //
  28 qed.