matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_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/rt_computation/csx_cpxs.ma".
  16 include "basic_2/rt_computation/csx_lsubr.ma".
  17 include "basic_2/rt_computation/lfsx_lpxs.ma".
  18 *)
  19 include "basic_2/rt_computation/lsubsx_lfsx.ma".
  20
  21 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
  22 (*
  23 axiom lpxs_trans: ∀h,G. Transitive … (lpxs h G).
  24 *)
  25
  26 (* Advanced properties ******************************************************)
  27
  28 (* Basic_2A1: uses: lsx_lref_be_lpxs *)
  29 lemma lfsx_pair_lpxs: ∀h,o,G,K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
  30                       ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
  31                       ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
  32 #h #o #G #K1 #V #H
  33 @(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
  34 @(lfsx_ind_lpxs … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
  35 @lfsx_intro_lpxs #Y #HY #HnY
  36 elim (lpxs_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
  37 elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
  38 [ /5 width=5 by lfsx_lfdeq_trans, lpxs_trans, lfdeq_pair/
  39 | @(IHV0 … HnV02) -IHV0 -HnV02
  40   [
  41   | /3 width=3 by lfsx_lpxs_trans, lfsx_cpxs_trans/
  42   | /2 width=3 by lpxs_trans/
  43   ]
  44
  45 (*
  46  @(lfsx_lpxs_trans … (K0.ⓑ{I}V2))
  47   [ @(IHV0 … HnV02 … HK10) -IHV0 -HnV02
  48     [
  49     | /2 width=3 by lfsx_cpxs_trans/
  50     ]
  51   |
  52   ]
  53 *)
  54
  55 (* Basic_2A1: uses: lsx_lref_be *)
  56 lemma lfsx_lref_pair: ∀h,o,G,K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
  57                       ∀I,L,i. ⬇*[i] L ≡ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
  58 #h #o #G #K #V #HV #HK #I #L #i #HLK
  59 @(lfsx_lifts … (#0) … HLK) -L /2 width=3 by lfsx_pair_lpxs/
  60 qed.
  61
  62 (* Main properties **********************************************************)
  63
  64 theorem csx_lsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
  65 #h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
  66 #Z #Y #X #IH #G #L * * //
  67 [ #i #HG #HL #HT #H destruct
  68   elim (csx_inv_lref … H) -H [ |*: * ]
  69   [ /2 width=1 by lfsx_lref_atom/
  70   | /2 width=3 by lfsx_lref_unit/
  71   | /4 width=6 by lfsx_lref_pair, fqup_lref/
  72   ]
  73 | #a #I #V #T #HG #HL #HT #H destruct
  74   elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by lfsx_bind_void/
  75 | #I #V #T #HG #HL #HT #H destruct
  76   elim (csx_fwd_flat … H) -H /3 width=1 by lfsx_flat/
  77 ]
  78 qed.