matita/matita/contribs/lambdadelta/apps_2/functional/flifts_flifts.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 "static_2/relocation/lifts_lifts.ma".
  16 include "apps_2/functional/flifts.ma".
  17
  18 (* GENERIC FUNCTIONAL RELOCATION ********************************************)
  19
  20 (* Main derived properties **************************************************)
  21
  22 theorem flifts_compose (f2) (f1) (T): ↑*[f2]↑*[f1]T = ↑*[f2∘f1]T.
  23 #f2 #f1 #T
  24 elim (lifts_total T f1) #U #HTU
  25 >(flifts_inv_lifts … HTU)
  26 /4 width=6 by flifts_inv_lifts, lifts_trans, sym_eq/
  27 qed.
  28
  29 (* Main derived properties with uniform relocation **************************)
  30
  31 theorem flifts_compose_uni (l2) (l1) (T): ↑[l2]↑[l1]T = ↑[l2+l1]T.
  32 #l2 #l1 #T >flifts_compose
  33 /4 width=1 by flifts_inv_lifts, lifts_uni, sym_eq/ qed.