matita/matita/contribs/lambdadelta/basic_2A/computation/lsx_lpxs.ma

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  14
  15 include "basic_2A/computation/lpxs_lpxs.ma".
  16 include "basic_2A/computation/lsx_alt.ma".
  17
  18 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
  23                         ∀Y,T. G ⊢ ⬊*[h, g, T, ⫯l] Y →
  24                         ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
  25                         G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L2.
  26 #h #g #a #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
  27 #L1 #HL1 #IHL1 #Y #T #H @(lsx_ind_alt … H) -Y
  28 #Y #HY #IHY #L2 #H #HL12 destruct @lsx_intro_alt
  29 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
  30 #HL10 #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ]
  31 [ #HnV elim (lleq_dec V L1 L2 l)
  32   [ #HV @(IHL1 … L0) /3 width=5 by lsx_lpxs_trans, lpxs_pair, lleq_canc_sn/ (**) (* full auto too slow *)
  33   | -HnV -HL10 /4 width=5 by lsx_lpxs_trans, lpxs_pair/
  34   ]
  35 | /3 width=4 by lpxs_pair/
  36 ]
  37 qed-.
  38
  39 lemma lsx_bind: ∀h,g,a,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
  40                 ∀T. G ⊢ ⬊*[h, g, T, ⫯l] L.ⓑ{I}V →
  41                 G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L.
  42 /2 width=3 by lsx_bind_lpxs_aux/ qed.
  43
  44 lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
  45                      ∀L2,T. G ⊢ ⬊*[h, g, T, l] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
  46                      G ⊢ ⬊*[h, g, ⓕ{I}V.T, l] L2.
  47 #h #g #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
  48 #L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind_alt … H) -L2
  49 #L2 #HL2 #IHL2 #HL12 @lsx_intro_alt
  50 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
  51 #HL10 #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
  52 [ #HnV elim (lleq_dec V L1 L2 l)
  53   [ #HV @(IHL1 … L0) /3 width=3 by lsx_lpxs_trans, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
  54   | -HnV -HL10 /3 width=4 by lsx_lpxs_trans/
  55   ]
  56 | /3 width=1 by/
  57 ]
  58 qed-.
  59
  60 lemma lsx_flat: ∀h,g,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
  61                 ∀T. G ⊢ ⬊*[h, g, T, l] L → G ⊢ ⬊*[h, g, ⓕ{I}V.T, l] L.
  62 /2 width=3 by lsx_flat_lpxs/ qed.