matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lpxs.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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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  13 (**************************************************************************)
  14
  15 include "basic_2/i_static/tc_lfxs_lex.ma".
  16 include "basic_2/rt_transition/cpx_lfeq.ma".
  17 include "basic_2/rt_computation/cpxs_lpx.ma".
  18 include "basic_2/rt_computation/lpxs.ma".
  19 include "basic_2/rt_computation/lfpxs.ma".
  20
  21 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
  22
  23 (* Properties with uncounted parallel rt-computation for local environments *)
  24
  25 lemma lfpxs_lpxs: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
  26 /2 width=1 by tc_lfxs_lex/ qed.
  27
  28 lemma lfpxs_lpxs_lfeq: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
  29                        ∀L2,T. L ≡[T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
  30 /2 width=3 by tc_lfxs_lex_lfeq/ qed.
  31
  32 (* Inversion lemmas with uncounted parallel rt-computation for local envs ***)
  33
  34 lemma lfpxs_inv_lpxs_lfeq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 →
  35                            ∃∃L. ⦃G, L1⦄ ⊢ ⬈*[h] L & L ≡[T] L2.
  36 /3 width=5 by lfpx_fsge_comp, lpx_cpxs_trans, lfeq_cpx_trans, tc_lfxs_inv_lex_lfeq/ qed-.