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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/rt_computation/lfpxs.ma".
  16 include "basic_2/rt_computation/csx_lsubr.ma".
  17 include "basic_2/rt_computation/lfsx_drops.ma".
  18 include "basic_2/rt_computation/lfsx_lfpxs.ma".
  19
  20 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
  21
  22 (* Advanced properties ******************************************************)
  23
  24 (* Basic_2A1: uses: lsx_lref_be_lpxs *)
  25 axiom lfsx_pair_lpxs: ∀h,o,G,K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
  26                       ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h, V] K2 →
  27                       ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
  28 (*
  29 #h #o #I #G #K1 #V #i #l #Hli #H @(csx_ind_alt … H) -V
  30 #V0 #_ #IHV0 #K2 #H @(lsx_ind … H) -K2
  31 #K0 #HK0 #IHK0 #HK10 #L0 #HLK0 @lsx_intro
  32 #L2 #HL02 #HnL02 elim (lpx_drop_conf … HLK0 … HL02) -HL02
  33 #Y #H #HLK2 elim (lpx_inv_pair1 … H) -H
  34 #K2 #V2 #HK02 #HV02 #H destruct
  35 elim (eq_term_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnL02 -HLK0 ]
  36 [ /4 width=8 by lpxs_strap1, lleq_lref/
  37 | @(IHV0 … HnV02 … HLK2) -IHV0 -HnV02 -HLK2
  38   /3 width=4 by lsx_cpx_trans_O, lsx_lpx_trans, lpxs_cpx_trans, lpxs_strap1/ (**) (* full auto too slow *)
  39 ]
  40 qed.
  41 *)
  42 (* Basic_2A1: uses: lsx_lref_be *)
  43 lemma lfsx_lref_pair: ∀h,o,G,K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
  44                       ∀I,L,i. ⬇*[i] L ≡ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
  45 #h #o #G #K #V #HV #HK #I #L #i #HLK
  46 @(lfsx_lifts … (#0) … HLK) -L /2 width=3 by lfsx_pair_lpxs/
  47 qed.
  48
  49 (* Main properties **********************************************************)
  50
  51 theorem csx_lsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
  52 #h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
  53 #Z #Y #X #IH #G #L * * //
  54 [ #i #HG #HL #HT #H destruct
  55   elim (csx_inv_lref … H) -H [ |*: * ]
  56   [ /2 width=1 by lfsx_lref_atom/
  57   | /2 width=3 by lfsx_lref_unit/
  58   | /4 width=6 by lfsx_lref_pair, fqup_lref/
  59   ]
  60 | #a #I #V #T #HG #HL #HT #H destruct
  61   elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by lfsx_bind_void/
  62 | #I #V #T #HG #HL #HT #H destruct
  63   elim (csx_fwd_flat … H) -H /3 width=1 by lfsx_flat/
  64 ]
  65 qed.