matita/matita/contribs/lambdadelta/apps_2/functional/mf_vpush_vlift.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 "apps_2/functional/mf_vlift_exteq.ma".
  16 include "apps_2/functional/mf_vpush.ma".
  17
  18 (* MULTIPLE FILLING PUSH ****************************************************)
  19
  20 (* Properties with multiple filling lift ************************************)
  21
  22 lemma mf_vpush_vlift_swap_O (v) (T) (l): ⇡[0←↑[↑l,1]T]⇡[l]v ≐⇡[↑l]⇡[0←T]v.
  23 #v #T #l #i
  24 elim (eq_or_gt i) #Hi destruct
  25 [ >mf_vpush_eq >mf_vlift_rw >mf_vpush_eq //
  26 | >(mf_vpush_gt … Hi) >mf_vlift_rw >mf_vlift_rw >(mf_vpush_gt … Hi)
  27   @mf_vlift_swap //
  28 ]
  29 qed.
  30
  31 lemma mf_vpush_vlift_swap_O_lref_O (v) (l): ⇡[0←#0]⇡[l]v ≐⇡[↑l]⇡[0←#0]v.
  32 #v #l @(mf_vpush_vlift_swap_O … (#0))
  33 qed.