matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma

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  14
  15 include "basic_2/computation/lpxs_lleq.ma".
  16 include "basic_2/computation/lpxs_lpxs.ma".
  17 include "basic_2/computation/lsx.ma".
  18
  19 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma lsx_lleq_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
  24                       ∀L2. L1 ⋕[T, 0] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
  25 #h #g #T #G #L1 #H @(lsx_ind … H) -L1
  26 #L1 #_ #IHL1 #L2 #HL12 @lsx_intro
  27 #K2 #HLK2 #HnLK2 elim (lleq_lpxs_trans … HL12 … HLK2) -HLK2
  28 /5 width=4 by lleq_canc_sn, lleq_trans/
  29 qed-.
  30
  31 lemma lsx_lpxs_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
  32                       ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
  33 #h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
  34 elim (lleq_dec T L1 L2 0) /3 width=4 by lsx_lleq_trans/
  35 qed-.
  36
  37 lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V. G ⊢ ⋕⬊*[h, g, V] L1 →
  38                      ∀L2,T. G ⊢ ⋕⬊*[h, g, T] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
  39                      G ⊢ ⋕⬊*[h, g, ⓕ{I}T.V] L2.
  40 #h #g #I #G #L1 #V #H @(lsx_ind … H) -L1
  41 #L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind … H) -L2
  42 #L2 #HL2 #IHL2 #HL12 @lsx_intro
  43 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
  44 #HL10 #H elim (nlleq_inv_flat … H) -H [ -HL2 -IHL1 | -HL1 -IHL2 ]
  45 [ /3 width=1 by/
  46 | #HnV elim (lleq_dec V L1 L2 0)
  47   [ #HV @(IHL1 … L0) /3 width=3 by lsx_lpxs_trans, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
  48   | -HnV -HL10 /3 width=4 by lsx_lpxs_trans/
  49 ]
  50 qed-.
  51
  52 lemma lsx_flat: ∀h,g,I,G,L,V. G ⊢ ⋕⬊*[h, g, V] L →
  53                 ∀T. G ⊢ ⋕⬊*[h, g, T] L → G ⊢ ⋕⬊*[h, g, ⓕ{I}T.V] L.
  54 /2 width=3 by lsx_flat_lpxs/ qed.