matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpcs_ltpss_dx.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/computation/cprs_ltpss_dx.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
  19
  20 (* Properties concerning dx partial unfold on local environments ************)
  21
  22 lemma cpcs_ltpss_dx_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
  23                           ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
  24 #L1 #L2 #d #e #HL12 #T1 #T2 #H
  25 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
  26 elim (cprs_ltpss_dx_conf … HT1 … HL12) -HT1 #U1 #HTU1 #H1
  27 elim (cprs_ltpss_dx_conf … HT2 … HL12) -L1 #U2 #HTU2 #H2
  28 elim (tpss_conf_eq … H1 … H2) -T #U #HU1 #HU2
  29 lapply (cprs_tpss_trans … HTU1 … HU1) -U1
  30 lapply (cprs_tpss_trans … HTU2 … HU2) -U2 /2 width=3/
  31 qed-.
  32
  33 lemma cpcs_ltpss_dx_tpss_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
  34                                ∀T,T2. L1 ⊢ T ⬌* T2 →
  35                                ∀T1. L2 ⊢ T ▶* [d, e] T1 →
  36                                L2 ⊢ T1 ⬌* T2.
  37 #L1 #L2 #d #e #HL12 #T #T2 #HT2 #T1 #HT1
  38 lapply (cpcs_ltpss_dx_conf … HL12 … HT2) -L1 #HT2
  39 lapply (cpcs_tpss_conf … HT1 … HT2) -T //
  40 qed-.
  41
  42 lemma cpcs_ltpss_dx_tpss2_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
  43                                 ∀T1,T2. L1 ⊢ T1 ⬌* T2 →
  44                                 ∀T3. L2 ⊢ T1 ▶* [d, e] T3 →
  45                                 ∀T4. L2 ⊢ T2 ▶* [d, e] T4 →
  46                                 L2 ⊢ T3 ⬌* T4.
  47 #L1 #L2 #d #e #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24
  48 lapply (cpcs_ltpss_dx_tpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32
  49 lapply (cpcs_tpss_strap1 … HT32 … HT24) -T2 //
  50 qed-.