matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.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 "delayed_updating/substitution/lift.ma".
  16 include "delayed_updating/syntax/path_depth.ma".
  17 include "ground/relocation/tr_pushs.ma".
  18
  19 (* LIFT FOR PATH ***********************************************************)
  20
  21 (* Basic constructions with depth ******************************************)
  22
  23 lemma pippo (p) (f):
  24       (⫯*[❘p❘]f) ∘ (↑[p]𝐢) = ↑[p]f.
  25 #p elim p -p
  26 [ #f <lift_rmap_empty <lift_rmap_empty <tr_pushs_zero
  27 | * [ #n ] #p #IH #f //
  28   <lift_rmap_d_sn <lift_rmap_d_sn <depth_d
  29   @(trans_eq … (IH …)) -IH
  30