matita/matita/contribs/lambda_delta/Basic_2/computation/cprs_tstc.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "Basic_2/grammar/tstc.ma".
  16 include "Basic_2/reducibility/cpr_lift.ma".
  17 include "Basic_2/reducibility/lcpr_cpr.ma".
  18 include "Basic_2/computation/cprs_cprs.ma".
  19
  20 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  21
  22 (* Forward lemmas involving same top term constructor ***********************)
  23
  24 lemma cpr_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡ U →
  25                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
  26                      L ⊢ ⓓV. ⓐV2. T ➡* U.
  27 #L #V1 #V #T #U #H #V2 #HV12
  28 elim (cpr_inv_appl1 … H) -H *
  29 [ -HV12 #V0 #X #_ #_ #H destruct /2 width=1/
  30 | -HV12 #V0 #W #T1 #T2 #_ #_ #H destruct
  31 | #V0 #V3 #W1 #W2 #T1 #T2 #HV10 #HW12 #HT12 #HV03 #H1 #H2 destruct
  32   lapply (cpr_lift (L.ⓓW1) … HV12 … HV03 … HV10) -V0 -HV12 /2 width=1/ #HV23
  33   lapply (lcpr_cpr_trans (L. ⓓW1) … HT12) -HT12 /2 width=1/ #HT12
  34   /4 width=1/
  35 ]
  36 qed-.