matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.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/reduction/cpx_cpys.ma".
  16 include "basic_2/computation/lpxs_cpye.ma".
  17 include "basic_2/computation/csx_alt.ma".
  18 include "basic_2/computation/lsx_lpxs.ma".
  19
  20 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  21
  22 (* Advanced properties ******************************************************)
  23
  24 axiom lpxs_cpye_csx_lsx: ∀h,g,G,L1,U. ⦃G, L1⦄ ⊢ ⬊*[h, g] U →
  25                          ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ∀T.  ⦃G, L2⦄ ⊢ T ▶*[0, ∞] 𝐍⦃U⦄ →
  26                          G ⊢ ⋕⬊*[h, g, T] L2.
  27 (*
  28 #h #g #G #L1 #U #H @(csx_ind_alt … H) -U
  29 #U0 #_ #IHU0 #L0 #HL10 #T #H0 @lsx_intro
  30 #L2 #HL02 #HnT elim (cpye_total G L2 T 0 (∞))
  31 #U2 #H2 elim (eq_term_dec U0 U2) #H destruct
  32 [ -IHU0
  33 | -HnT /4 width=9 by lpxs_trans, lpxs_cpxs_trans, cpx_cpye_fwd_lpxs/
  34 ]
  35 *)
  36 (* Main properties **********************************************************)
  37
  38 lemma csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → G ⊢ ⋕⬊*[h, g, T] L.
  39 #h #g #G #L #T #HT elim (cpye_total G L T 0 (∞))
  40 #U #HTU elim HTU
  41 /4 width=5 by lpxs_cpye_csx_lsx, csx_cpx_trans, cpys_cpx/
  42 qed.