matita/matita/contribs/lambdadelta/basic_2A/etc/lsubr/lpss_ldrop.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/relocation/fsup.ma".
  16 include "basic_2/relocation/ldrop_lpx_sn.ma".
  17 include "basic_2/substitution/cpss_lift.ma".
  18 include "basic_2/substitution/lpss.ma".
  19
  20 (* SN PARALLEL SUBSTITUTION FOR LOCAL ENVIRONMENTS **************************)
  21
  22 (* Properies on local environment slicing ***********************************)
  23
  24 lemma lpss_ldrop_conf: dropable_sn lpss.
  25 /3 width=5 by lpx_sn_deliftable_dropable, cpss_inv_lift1/ qed-.
  26
  27 lemma ldrop_lpss_trans: dedropable_sn lpss.
  28 /3 width=9 by lpx_sn_liftable_dedropable, cpss_lift/ qed-.
  29
  30 lemma lpss_ldrop_trans_O1: dropable_dx lpss.
  31 /2 width=3 by lpx_sn_dropable/ qed-.
  32
  33 (* Properties on context-sensitive parallel substitution for terms **********)
  34
  35 lemma fsup_cpss_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ▶* U2 →
  36                        ∃∃L,U1. L1 ⊢ ▶* L & L ⊢ T1 ▶* U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
  37 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [2: * ] [1,2,3,4,5: /3 width=5/ ]
  38 [ #L #K #U #T #d #e #HLK #HUT #He #U2 #HU2
  39   elim (lift_total U2 d e) #T2 #HUT2
  40   lapply (cpss_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9/
  41 | #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
  42   elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HT2
  43   elim (lift_total T d e) #U #HTU
  44   elim (ldrop_lpss_trans … HLK1 … HK1) -HLK1 -HK1 #L2 #HL12 #HL2K
  45   lapply (cpss_lift … HT1 … HL2K … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
  46 ]
  47 qed-.