matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_ldrop.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 "basic_2/reduction/cpx.ma".
  16
  17 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
  18
  19 include "basic_2/substitution/lpss_ldrop.ma".
  20 include "basic_2/substitution/fsups.ma".
  21
  22 lemma fsup_cpss_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ▶* U2 →
  23                        ∃∃U1. L1 ⊢ T1 ▶* U1 & ⦃L1, U1⦄ ⊃ ⦃L2, U2⦄.
  24 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [2: * ] [1,2,3,4,5: /3 width=5/ ]
  25 [ * #L1
  26   [ #V2 #U2 #HVU2
  27     elim (lift_total U2 0 1) #W2 #HUW2
  28     @(ex2_intro … W2) /2 width=7/
  29     @(fsup_ldrop … L1 … HUW2) /2 width=1/
  30   | #W #U2 #H
  31     @(ex2_intro … (#0)) /2 width=7/
  32
  33 | #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
  34   elim (IHT12 … HTU2) -IHT12 -HTU2 #T #HT1 #HT2
  35   elim (lift_total T d e) #U #HTU
  36   lapply (cpss_lift … HT1 … HLK1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
  37 ]
  38 qed-.
  39
  40
  41
  42 (*
  43 include "basic_2/relocation/lift_lift.ma".
  44 include "basic_2/substitution/fsups.ma".
  45 *)
  46 (*
  47 lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
  48                        ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
  49                        ∃∃L,U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
  50
  51 *)
  52 lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
  53                        ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
  54                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃ ⦃L2, U2⦄.
  55 #h #g #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2
  56 [ * #L1 #V1 #U2 #l #H
  57   elim (lift_total U2 0 1) #W2 #HUW2
  58 (*
  59   [ @(ex2_intro … W2) [ @(cpx_ssta … l) @(ssta_ldef … H) //
  60                       | @(fsups_ldrop … L1 … HUW2) /2 width=1/
  61 *)
  62 |
  63 | #a #I #L1 #V1 #T1 #U2 #l #HT1
  64   @(ex2_intro … (ⓑ{a,I}V1.U2)) /2 width=1/