matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_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/reduction/ibfr.ma".
  16
  17 include "delayed_updating/substitution/fsubst_lift.ma".
  18 include "delayed_updating/substitution/fsubst_eq.ma".
  19 include "delayed_updating/substitution/lift_prototerm_after.ma".
  20 include "delayed_updating/substitution/lift_path_structure.ma".
  21 include "delayed_updating/substitution/lift_path_closed.ma".
  22 include "delayed_updating/substitution/lift_path_guard.ma".
  23 include "delayed_updating/substitution/lift_rmap_closed.ma".
  24
  25 include "ground/relocation/tr_uni_compose.ma".
  26 include "ground/relocation/tr_compose_eq.ma".
  27
  28 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
  29
  30 (* Constructions with lift **************************************************)
  31
  32 theorem ibfr_lift_bi (f) (t1) (t2) (r):
  33         t1 ➡𝐢𝐛𝐟[r] t2 → 🠡[f]t1 ➡𝐢𝐛𝐟[🠡[f]r] 🠡[f]t2.
  34 #f #t1 #t2 #r
  35 * #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
  36 @(ex7_5_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔)]b) (🠡[🠢[f](p◖𝗔●b◖𝗟)]q) (🠢[f](p●𝗔◗b)＠❨m❩) (🠢[f](p●𝗔◗b●𝗟◗q)＠§❨n❩))
  37 [ -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
  38 | -Hb -Hm -Hn -Ht1 -Ht2
  39   /2 width=1 by lift_path_guard/
  40 | -Hp -Hm -Hn -Ht1 -Ht2 //
  41 | -Hp -Hb -Hn -Ht1 -Ht2
  42   /2 width=1 by lift_path_closed/
  43 | -Hp -Hb -Hm -Ht1 -Ht2
  44   /2 width=1 by lift_path_rmap_closed_L/
  45 | lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -Hp -Hn
  46   <lift_path_d_dx #Ht1 //
  47 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1 -Hp
  48   @(subset_eq_trans … Ht2) -t2
  49   @(subset_eq_trans … (lift_term_fsubst …))
  50   @fsubst_eq_repl [ // | <lift_path_append // ]
  51   @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
  52   [ @lift_term_grafted_S | skip ]
  53   @(subset_eq_trans … (lift_term_after …))
  54   @(subset_eq_canc_dx … (lift_term_after …))
  55   @lift_term_eq_repl_sn
  56 (* Note: crux of the proof begins *)
  57   @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
  58   @tr_compose_eq_repl
  59   [ <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
  60     >(nap_plus_lift_rmap_append_closed_Lq_dx … Hn) -Hn //
  61   | >lift_rmap_A_dx >nsucc_unfold
  62     /2 width=2 by tls_succ_plus_lift_rmap_append_closed_bLq_dx/
  63   ]
  64 (* Note: crux of the proof ends *)
  65 ]
  66 qed.