matita/matita/contribs/lambda_delta/basic_2/reducibility/lcpr_lcpr.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/unfold/ltpss_ltpss.ma".
  16 include "basic_2/reducibility/ltpr_ltpss.ma".
  17 include "basic_2/reducibility/ltpr_ltpr.ma".
  18 include "basic_2/reducibility/lcpr.ma".
  19
  20 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***************)
  21
  22 (* Main properties **********************************************************)
  23
  24 theorem lcpr_conf: ∀L0,L1,L2. L0 ⊢ ➡ L1 → L0 ⊢ ➡ L2 →
  25                    ∃∃L. L1 ⊢ ➡ L & L2 ⊢ ➡ L.
  26 #K0 #L1 #L2 * #K1 #HK01 #HKL1 * #K2 #HK02 #HKL2
  27 lapply (ltpr_fwd_length … HK01) #H
  28 >(ltpr_fwd_length … HK02) in H; #H
  29 elim (ltpr_conf … HK01 … HK02) -K0 #K #HK1 #HK2
  30 lapply (ltpss_fwd_length … HKL1) #H1
  31 lapply (ltpss_fwd_length … HKL2) #H2
  32 >H1 in HKL1 H; -H1 #HKL1
  33 >H2 in HKL2; -H2 #HKL2 #H
  34 elim (ltpr_ltpss_conf … HKL1 … HK1) -K1 #K1 #HK1 #HLK1
  35 elim (ltpr_ltpss_conf … HKL2 … HK2) -K2 #K2 #HK2 #HLK2
  36 elim (ltpss_conf … HK1 … HK2) -K #K #HK1 #HK2
  37 lapply (ltpr_fwd_length … HLK1) #H1
  38 lapply (ltpr_fwd_length … HLK2) #H2
  39 /3 width=5/
  40 qed.