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/computation/lpxs_lleq.ma".
  16 include "basic_2/computation/csx_alt.ma".
  17 include "basic_2/computation/lsx_lpxs.ma".
  18
  19 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  20
  21 (* Advanced forward lemmas **************************************************)
  22 (*
  23 lemma lsx_fwd_bind_dx_lpxs: ∀h,g,a,I,G,L1,V. ⦃G, L1⦄ ⊢ ⬊*[h, g] V →
  24                             ∀L2,T. G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
  25                             G ⊢ ⋕⬊*[h, g, T] L2.ⓑ{I}V.
  26 #h #g #a #I #G #L1 #V #H @(csx_ind_alt … H) -V
  27 #V1 #_ #IHV1 #L2 #T #H @(lsx_ind … H) -L2
  28 #L2 #HL2 #IHL2 #HL12 @lsx_intro
  29 #Y #H #HnT elim (lpxs_inv_pair1 … H) -H
  30 #L3 #V3 #HL23 #HV13 #H destruct
  31 lapply (lpxs_trans … HL12 … HL23) #HL13
  32 elim (eq_term_dec V1 V3)
  33 [ -HV13 -HL2 -IHV1 -HL12 #H destruct
  34   @IHL2 -IHL2 // -HL23 -HL13 /3 width=2 by lleq_fwd_bind_O/
  35 | -IHL2 -HL23 -HnT #HnV13
  36   @(IHV1 … HnV13) -IHV1 -HnV13 /2 width=3 by lpxs_cpxs_trans/ -HL12 -HL13 -HV13
  37   @(lsx_lpxs_trans) … HL2)
  38 *)
  39
  40 (* Advanced inversion lemmas ************************************************)
  41
  42
  43
  44 (* Main properties **********************************************************)
  45
  46 axiom csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → G ⊢ ⋕⬊*[h, g, T] L.
  47 (*
  48 #h #g #G #L #T @(fqup_wf_ind_eq … G L T) -G -L -T
  49 #G1 #L1 #T1 #IH #G2 #L2 * *
  50 [ #k #HG #HL #HT destruct //
  51 | #i #HG #HL #HT destruct
  52   #H
  53 | #p #HG #HL #HT destruct //
  54 | #a #I #V2 #T2 #HG #HL #HT #H destruct
  55   elim (csx_fwd_bind … H) -H
  56   #HV2 #HT2
  57 | #I #V2 #T2 #HG #HL #HT #H destruct
  58   elim (csx_fwd_flat … H) -H /3 width=1 by lsx_flat/
  59 *)