matita/matita/contribs/lambdadelta/ground/relocation/tr_compose_pap.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/relocation/tr_pap_tls.ma".
  17
  18 (* COMPOSITION FOR TOTAL RELOCATION MAPS ************************************)
  19
  20 (* Constructions with tr_pap ************************************************)
  21
  22 (*** compose_apply *)
  23 lemma tr_compose_pap (i) (f1) (f2):
  24       f2＠⧣❨f1＠⧣❨i❩❩ = (f2∘f1)＠⧣❨i❩.
  25 #i elim i -i
  26 [ * #p1 #f1 #f2
  27   <tr_compose_unfold <tr_pap_unit <tr_pap_unit //
  28 | #i #IH * #p1 #f1 #f2
  29   <tr_compose_unfold <tr_pap_succ <tr_pap_succ //
  30 ]
  31 qed.