matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.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 include "delayed_updating/substitution/fsubst_lift.ma".
  18 include "delayed_updating/substitution/fsubst_eq.ma".
  19 include "delayed_updating/substitution/lift_constructors.ma".
  20 include "delayed_updating/substitution/lift_preterm_eq.ma".
  21 include "delayed_updating/substitution/lift_structure_depth.ma".
  22 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
  23 include "delayed_updating/syntax/path_structure_depth.ma".
  24 include "ground/relocation/tr_pap_pushs.ma".
  25
  26 (* DELAYED FOCUSED REDUCTION ************************************************)
  27
  28 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
  29       t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
  30 #f #p #q #t1 #t2 #H0t1
  31 * #b #n * #Hb #Hn  #Ht1 #Ht2
  32 @(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
  33 [ //
  34 | #g <lift_rmap_structure <depth_structure
  35   >tr_pushs_swap <tr_pap_pushs_le //
  36 | lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
  37   <lift_path_d_empty_dx //
  38 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
  39   @(subset_eq_trans … Ht2) -t2
  40   @(subset_eq_trans … (lift_fsubst …))
  41   [ <structure_append <structure_A_sn <structure_append <structure_L_sn
  42     @fsubst_eq_repl [ // ]
  43     @(subset_eq_trans … (lift_iref …))
  44     @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
  45     [ @lift_grafted_S /2 width=2 by ex_intro/ | skip ]
  46     @(subset_eq_trans … (lift_term_after …))
  47     @(subset_eq_canc_dx … (lift_term_after …))
  48     @lift_term_eq_repl_sn -t1
  49   | //
  50   | /2 width=2 by ex_intro/
  51   | //
  52   ]
  53 ]