matita/matita/contribs/lambdadelta/basic_2/etc/rdsx_csx.etc

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   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                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/csx_lsubr.ma".
  16 include "basic_2/rt_computation/csx_cpxs.ma".
  17 include "basic_2/rt_computation/sdsx_rdsx.ma".
  18
  19 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma rdsx_pair_lpxs (h) (I) (G):
  24                      ∀K1,V1. G ⊢ ⬈*[h,V1] 𝐒⦃K1⦄ →
  25                      ∀V2. ⦃G,K1⦄ ⊢ ⬈*[h] 𝐒⦃V2⦄ →
  26                      (∀K. ⦃G,K1⦄ ⊢ ⬈*[h] K → ⦃G,K⦄ ⊢ V1 ⬈*[h] V2) →
  27                      G ⊢ ⬈*[h,#0] 𝐒⦃K1.ⓑ{I}V2⦄.
  28 #h #I #G #K1 #V1 #H
  29 @(rdsx_ind_lpxs … H) -K1 #K1 #_ #IHK #V2 #H
  30 @(csx_ind_cpxs … H) -V2 #V2 #HV2 #IHV #HK
  31 @rdsx_intro_lpxs #Y #HY #HnY
  32 elim (lpxs_inv_pair_sn … HY) -HY #K3 #V3 #HK13 #HV23 #H destruct
  33 elim (tdeq_dec V2 V3)
  34 [ -IHV -HV23 #HV23
  35   @(rdsx_rdeq_trans … (K3.ⓑ{I}V2)) [| /2 width=1 by rdeq_pair_refl/ ]
  36   @(IHK … HK13) -IHK
  37   [
  38   |
  39   | /3 width=3 by lpxs_trans/
  40   ]
  41 | -IHK -HnY #HnV23
  42   @(rdsx_lpxs_trans … (K1.ⓑ{I}V3)) [| /2 width=1 by lpxs_bind_refl_dx/ ]
  43   @(IHV … HV23 HnV23) -IHV -HnV23
  44   #K #HK