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

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