matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lpss.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/substitution/lpss_cpss.ma".
  16 include "basic_2/reduction/lpr_lpss.ma".
  17 include "basic_2/computation/cprs.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  20
  21 (* Properties on parallel substitution for terms ****************************)
  22
  23 (* Basic_1: was: pr3_subst1 *)
  24 lemma cprs_cpss_conf: ∀L,T0,T1. L ⊢ T0 ➡* T1 → ∀T2. L ⊢ T0 ▶* T2 →
  25                       ∃∃T. L ⊢ T1 ▶* T & L ⊢ T2 ➡* T.
  26 #L @TC_strip1 /2 width=3 by cpr_cpss_conf/ qed-. (**) (* auto /3 width=3/ fails because a δ-expansion gets in the way *)
  27
  28 (* Properties on sn parallel substitution for local environments ************)
  29
  30 lemma cprs_lpss_conf_dx: ∀L0,T0,T1. L0 ⊢ T0 ➡* T1 → ∀L1. L0 ⊢ ▶* L1 →
  31                          ∃∃T. L1 ⊢ T1 ▶* T & L1 ⊢ T0 ➡* T.
  32 #L0 #T0 #T1 #H elim H -T1
  33 [ #T1 #HT01 #L1 #HL01
  34   elim (cpr_lpss_conf_dx … HT01 … HL01) -L0 /3 width=3/
  35 | #T #T1 #_ #HT1 #IHT0 #L1 #HL01
  36   elim (IHT0 … HL01) #T2 #HT2 #HT02
  37   elim (cpr_lpss_conf_dx … HT1 … HL01) -L0 #T3 #HT13 #HT3
  38   elim (cpr_cpss_conf … HT3 … HT2) -T #T #HT3 #HT2
  39   lapply (cpss_trans … HT13 … HT3) -T3
  40   lapply (cprs_strap1 … HT02 … HT2) -T2 /2 width=3/
  41 ]
  42 qed-.
  43
  44 lemma cprs_lpss_conf_sn: ∀L0,T0,T1. L0 ⊢ T0 ➡* T1 → ∀L1. L0 ⊢ ▶* L1 →
  45                          ∃∃T. L0 ⊢ T1 ▶* T & L1 ⊢ T0 ➡* T.
  46 #L0 #T0 #T1 #HT01 #L1 #HL01
  47 elim (cprs_lpss_conf_dx … HT01 … HL01) -HT01 #T #HT1
  48 lapply (lpss_cpss_trans … HL01 … HT1) -HT1 /2 width=3/
  49 qed-.