matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fdeq.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 "static_2/static/fdeq.ma".
  16 include "basic_2/rt_transition/cpx_rdeq.ma".
  17 include "basic_2/rt_transition/rpx_rdeq.ma".
  18
  19 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
  20
  21 (* Properties with degree-based equivalence for closures ********************)
  22
  23 lemma fdeq_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T⦄ →
  24                       ∀T2. ⦃G2, L2⦄ ⊢ T ⬈[h] T2 →
  25                       ∃∃T0. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T0 & ⦃G1, L1, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
  26 #h #o #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
  27 elim (fdeq_inv_gen_dx … H) -H #H #HL12 #HT1 destruct
  28 elim (rdeq_cpx_trans … HL12 … HT2) #T0 #HT0 #HT02
  29 lapply (cpx_rdeq_conf_dx … HT2 … HL12) -HL12 #HL12
  30 elim (tdeq_cpx_trans … HT1 … HT0) -T #T #HT1 #HT0
  31 /4 width=5 by fdeq_intro_dx, tdeq_trans, ex2_intro/
  32 qed-.