matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.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/static/lfdeq_fqus.ma".
  16 include "basic_2/rt_transition/cpx_lfdeq.ma".
  17 include "basic_2/rt_transition/lfpx_lfdeq.ma".
  18 include "basic_2/rt_transition/fpb.ma".
  19
  20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  21
  22 (* Properties with degree-based equivalence for local environments **********)
  23
  24 (* Basic_2A1: was just: lleq_fpb_trans *)
  25 lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≛[h, o, T] K2 →
  26                        ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
  27                        ∃∃L1,U0. ⦃F, K1, T⦄ ≻[h, o] ⦃G, L1, U0⦄ & U0 ≛[h, o] U & L1 ≛[h, o, U] L2.
  28 #h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
  29 [ #G #L2 #U #H2 elim (lfdeq_fqu_trans … H2 … HT) -K2
  30   /3 width=5 by fpb_fqu, ex3_2_intro/
  31 | #U #HTU #HnTU elim (lfdeq_cpx_trans … HT … HTU) -HTU
  32   /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf, ex3_2_intro/
  33 | #L2 #HKL2 #HnKL2 elim (lfdeq_lfpx_trans … HKL2 … HT) -HKL2
  34   /6 width=5 by fpb_lfpx, (* 2x *) lfdeq_canc_sn, ex3_2_intro/
  35 ]
  36 qed-.