matita/matita/contribs/lambdadelta/ground/relocation/tr_compose_tls.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_compose.ma".
  16 include "ground/lib/stream_tls_plus.ma".
  17 include "ground/arith/nat_plus_rplus.ma".
  18 include "ground/arith/nat_rplus_pplus.ma".
  19
  20 (* COMPOSITION FOR TOTAL RELOCATION MAPS ************************************)
  21
  22 (* Advanced constructions with stream_tls ***********************************)
  23
  24 lemma tr_compose_tls (p) (f1) (f2):
  25       (⇂*[f1@❨p❩]f2)∘(⇂*[p]f1) = ⇂*[p](f2∘f1).
  26 #p elim p -p [| #p #IH ] * #q1 #f1 #f2 //
  27 <tr_compose_unfold <tr_pap_succ
  28 >nsucc_inj <stream_tls_succ_lcons <stream_tls_succ_lcons
  29 <IH -IH >nrplus_inj_dx >nrplus_inj_sn <stream_tls_plus //
  30 qed.