matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.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/unwind/unwind2_path.ma".
  16 include "delayed_updating/unwind/unwind2_rmap_lift.ma".
  17 include "delayed_updating/substitution/lift_path_structure.ma".
  18
  19 (* TAILED UNWIND FOR PATH ***************************************************)
  20
  21 (* Constructions with lift_path *********************************************)
  22
  23 lemma lift_unwind2_path_after (g) (f) (p):
  24       🠡[g]▼[f]p = ▼[g∘f]p.
  25 #g #f * // * [ #k ] #p //
  26 <unwind2_path_d_dx <unwind2_path_d_dx <lift_path_d_dx
  27 <lift_path_structure >tr_compose_pap
  28 /4 width=1 by tr_pap_eq_repl, eq_f2, eq_f/
  29 qed.
  30
  31 lemma unwind2_lift_path_after (g) (f) (p):
  32       ▼[g]🠡[f]p = ▼[g∘f]p.
  33 #g #f * // * [ #k ] #p
  34 [ <unwind2_path_d_dx <unwind2_path_d_dx
  35   <structure_lift_path >tr_compose_pap
  36   /4 width=1 by tr_pap_eq_repl, eq_f2, eq_f/
  37 | <unwind2_path_m_dx <unwind2_path_m_dx //
  38 | <unwind2_path_L_dx <unwind2_path_L_dx //
  39 | <unwind2_path_A_dx <unwind2_path_A_dx //
  40 | <unwind2_path_S_dx <unwind2_path_S_dx //
  41 ]
  42 qed.