matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr_cpr.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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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/unfold/ltpss_sn_ltpss_sn.ma".
  16 include "basic_2/reducibility/cpr.ma".
  17 include "basic_2/reducibility/lfpr.ma".
  18
  19 (* FOCALIZED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS **********************)
  20
  21 (* Advanced properties ****************************************************)
  22
  23 lemma lfpr_pair_cpr: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡ V2 →
  24                      ∀I. ⦃L1. ⓑ{I} V1⦄ ➡ ⦃L2. ⓑ{I} V2⦄.
  25 #L1 #L2 * #L #HL1 #HL2 #V1 #V2 *
  26 <(ltpss_sn_fwd_length … HL2) #V #HV1 #HV2 #I
  27 lapply (ltpss_sn_tpss_trans_eq … HV2 … HL2) -HV2 #V2
  28 @(ex2_1_intro … (L.ⓑ{I}V)) /2 width=1/ (**) (* explicit constructor *)
  29 qed.