matita/matita/contribs/lambdadelta/basic_2/etc_2A1/delift/cpr_delift.etc

   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 "basic_2/unfold/thin_delift.ma".
  16 include "basic_2/reducibility/tpr_delift.ma".
  17 include "basic_2/reducibility/cpr.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  20
  21 (* Properties on inverse basic term relocation ******************************)
  22
  23 (* Basic_1: was only: pr2_gen_cabbr *)
  24 lemma thin_cpr_delift_conf: ∀L,U1,U2. L ⊢ U1 ➡ U2 →
  25                             ∀K,d,e. ▼*[d, e] L ≡ K → ∀T1. L ⊢ ▼*[d, e] U1 ≡ T1 →
  26                             ∃∃T2. K ⊢ T1 ➡ T2 & L ⊢ ▼*[d, e] U2 ≡ T2.
  27 #L #U1 #U2 * #U #HU1 #HU2 #K #d #e #HLK #T1 #HTU1
  28 elim (tpr_delift_conf … HU1 … HTU1) -U1 #T #HT1 #HUT
  29 elim (le_or_ge (|L|) d) #Hd
  30 [ elim (thin_delift_tpss_conf_le … HU2 … HUT … HLK ?)
  31 | elim (le_or_ge (|L|) (d+e)) #Hde
  32   [ elim (thin_delift_tpss_conf_le_up … HU2 … HUT … HLK ? ? ?)
  33   | elim (thin_delift_tpss_conf_be … HU2 … HUT … HLK ? ?)
  34   ]
  35 ] -U -HLK // -Hd [2,3: -Hde] #T2 #HT2
  36 lapply (cpr_intro … HT1 HT2) -T /2 width=3/
  37 qed.