matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.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_path.ma".
  16 include "ground/lib/list_length.ma".
  17
  18 (* LIFT FOR PATH ************************************************************)
  19
  20 (* Constructions with list_length *******************************************)
  21
  22 lemma lift_path_length (f) (p):
  23       ❘p❘ = ❘↑[f]p❘.
  24 #f #p elim p -p // * [ #k ] #p #IH
  25 [ <lift_path_d_dx
  26 | <lift_path_m_dx
  27 | <lift_path_L_dx
  28 | <lift_path_A_dx
  29 | <lift_path_S_dx
  30 ]
  31 >list_length_lcons >list_length_lcons //
  32 qed.