matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_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/dfr.ma".
  16 include "delayed_updating/reduction/ifr.ma".
  17
  18 include "delayed_updating/substitution/fsubst_lift.ma".
  19 include "delayed_updating/substitution/fsubst_eq.ma".
  20 include "delayed_updating/substitution/lift_constructors.ma".
  21 include "delayed_updating/substitution/lift_prototerm_eq.ma".
  22 include "delayed_updating/substitution/lift_path_head.ma".
  23 include "delayed_updating/substitution/lift_rmap_head.ma".
  24
  25 (* DELAYED FOCUSED REDUCTION ************************************************)
  26
  27 (* Constructions with lift **************************************************)
  28
  29 theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
  30         t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐝𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
  31 #f #p #q #t1 #t2
  32 * #n * #H1n #Ht1 #Ht2
  33 @(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨n❩)) @and3_intro
  34 [ -Ht1 -Ht2
  35   <lift_rmap_L_dx >lift_path_L_sn
  36   >list_append_rcons_sn in H1n; <reverse_append #H1n
  37   <(lift_path_head … H1n) -H1n //
  38 | lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1n
  39   <lift_path_d_dx #Ht1 //
  40 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
  41   @(subset_eq_trans … Ht2) -t2
  42   @(subset_eq_trans … (lift_term_fsubst …))
  43   @fsubst_eq_repl [ // | // ]
  44   @(subset_eq_trans … (lift_term_iref …))
  45   @iref_eq_repl
  46   @(subset_eq_canc_sn … (lift_term_grafted_S …))
  47   @lift_term_eq_repl_sn
  48 (* Note: crux of the proof begins *)
  49   >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
  50   /2 width=1 by tls_lift_rmap_append_closed/
  51 (* Note: crux of the proof ends *)
  52 ]
  53 qed.