matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.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/grammar/tstc.ma".
  16 (*
  17 include "Basic_2/reducibility/cpr_lift.ma".
  18 include "Basic_2/reducibility/lcpr_cpr.ma".
  19 *)
  20 include "Basic_2/computation/cprs_cprs.ma".
  21
  22 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  23
  24 (* Forward lemmas involving same top term constructor ***********************)
  25 (*
  26 lemma cpr_fwd_beta: ∀L,V,W,T,U. L ⊢ ⓐV. ⓛW. T ➡ U →
  27                     ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⓓV. T ➡* U.
  28 #L #V #W #T #U #H
  29 elim (cpr_inv_appl1 … H) -H *
  30 [ #V0 #X #_ #_ #H destruct /2 width=1/
  31 | #V0 #W0 #T1 #T2 #HV0 #HT12 #H1 #H2 destruct
  32   lapply (lcpr_cpr_trans (L. ⓓV) … HT12) -HT12 /2 width=1/ /3 width=1/
  33 | #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #H destruct
  34 ]
  35 qed-.
  36
  37 lemma cpr_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡ U →
  38                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
  39                      L ⊢ ⓓV. ⓐV2. T ➡* U.
  40 #L #V1 #V #T #U #H #V2 #HV12
  41 elim (cpr_inv_appl1 … H) -H *
  42 [ -HV12 #V0 #X #_ #_ #H destruct /2 width=1/
  43 | -HV12 #V0 #W #T1 #T2 #_ #_ #H destruct
  44 | #V0 #V3 #W1 #W2 #T1 #T2 #HV10 #HW12 #HT12 #HV03 #H1 #H2 destruct
  45   lapply (cpr_lift (L.ⓓW1) … HV12 … HV03 … HV10) -V0 -HV12 /2 width=1/ #HV23
  46   lapply (lcpr_cpr_trans (L. ⓓW1) … HT12) -HT12 /2 width=1/ #HT12
  47   /4 width=1/
  48 ]
  49 qed-.
  50 *)
  51 lemma cprs_fwd_tau: ∀L,W,T,U. L ⊢ ⓣW. T ➡* U →
  52                     ⓣW. T ≃ U ∨ L ⊢ T ➡* U.
  53 #L #W #T #U #H
  54 elim (cprs_inv_cast1 … H) -H /2 width=1/ *
  55 #W0 #T0 #_ #_ #H destruct /2 width=1/
  56 qed-.