matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lfpr_lfpr.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/reducibility/ltpr_ltpss_sn.ma".
  16 include "basic_2/reducibility/ltpr_ltpr.ma".
  17 include "basic_2/reducibility/lfpr.ma".
  18
  19 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
  20
  21 (* Main properties **********************************************************)
  22
  23 theorem lfpr_conf: ∀L0,L1,L2. ⦃L0⦄ ➡ ⦃L1⦄ → ⦃L0⦄ ➡ ⦃L2⦄ →
  24                    ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
  25 #K0 #L1 #L2 * #K1 #HK01 #HKL1 * #K2 #HK02 #HKL2
  26 lapply (ltpr_fwd_length … HK01) #H
  27 >(ltpr_fwd_length … HK02) in H; #H
  28 elim (ltpr_conf … HK01 … HK02) -K0 #K #HK1 #HK2
  29 lapply (ltpss_sn_fwd_length … HKL1) #H1
  30 lapply (ltpss_sn_fwd_length … HKL2) #H2
  31 >H1 in HKL1 H; -H1 #HKL1
  32 >H2 in HKL2; -H2 #HKL2 #H
  33 elim (ltpr_ltpss_sn_conf … HKL1 … HK1) -K1 #K1 #HK1 #HLK1
  34 elim (ltpr_ltpss_sn_conf … HKL2 … HK2) -K2 #K2 #HK2 #HLK2
  35 elim (ltpss_sn_conf … HK1 … HK2) -K #K #HK1 #HK2
  36 lapply (ltpr_fwd_length … HLK1) #H1
  37 lapply (ltpr_fwd_length … HLK2) #H2
  38 /3 width=5/
  39 qed.