matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llsx_llpxs.etc

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  14
  15 include "basic_2/computation/llpxs_llpxs.ma".
  16 include "basic_2/computation/llsx_alt.ma".
  17
  18 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 fact llsx_bind_llpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 →
  23                           ∀Y,T. G ⊢ ⋕⬊*[h, g, T, ⫯d] Y →
  24                           ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g, ⓑ{a,I}V.T, d] L2 →
  25                           G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L2.
  26 #h #g #a #I #G #L1 #V #d #H @(llsx_ind_alt … H) -L1
  27 #L1 #HL1 #IHL1 #Y #T #H @(llsx_ind_alt … H) -Y
  28 #Y #HY #IHY #L2 #H #HL12 destruct @llsx_intro_alt
  29 #L0 #HL20 lapply (llpxs_fwd_bind_dx … HL20)
  30 lapply (llpxs_trans … HL12 … HL20)
  31 #HL10 #HT #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ]
  32 [ #HnV elim (lleq_dec V L1 L2 d)
  33   [  -HL20 #HV @(IHL1 … L0)
  34      /3 width=4 by llsx_llpxs_trans, llpxs_fwd_bind_sn, lleq_canc_sn/ (**) (* full auto too slow *)
  35   | -HnV -HL10
  36      /3 width=4 by llsx_llpxs_trans, llpxs_fwd_bind_sn/
  37   ]
  38 | /3 width=4 by/
  39 ]
  40 qed-.
  41
  42 lemma llsx_bind: ∀h,g,a,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L →
  43                  ∀T. G ⊢ ⋕⬊*[h, g, T, ⫯d] L.ⓑ{I}V →
  44                  G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L.
  45 /2 width=3 by llsx_bind_llpxs_aux/ qed.
  46
  47 lemma llsx_flat_llpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 →
  48                        ∀L2,T. G ⊢ ⋕⬊*[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, ⓕ{I}V.T, d] L2 →
  49                        G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L2.
  50 #h #g #I #G #L1 #V #d #H @(llsx_ind_alt … H) -L1
  51 #L1 #HL1 #IHL1 #L2 #T #H @(llsx_ind_alt … H) -L2
  52 #L2 #HL2 #IHL2 #HL12 @llsx_intro_alt
  53 #L0 #HL20 lapply (llpxs_fwd_flat_dx … HL20)
  54 lapply (llpxs_trans … HL12 … HL20)
  55 #HL10 #HT #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
  56 [ #HnV elim (lleq_dec V L1 L2 d)
  57   [ #HV @(IHL1 … L0) /3 width=3 by llsx_llpxs_trans, llpxs_fwd_flat_sn, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
  58   | -HnV -HL10 /3 width=4 by llsx_llpxs_trans, llpxs_fwd_flat_sn/
  59   ]
  60 | /3 width=1 by/
  61 ]
  62 qed-.
  63
  64 lemma llsx_flat: ∀h,g,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L →
  65                  ∀T. G ⊢ ⋕⬊*[h, g, T, d] L → G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L.
  66 /2 width=3 by llsx_flat_llpxs/ qed.