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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/static/lfdeq_lfdeq.ma".
  16 include "basic_2/rt_transition/lfpx_lfdeq.ma".
  17 include "basic_2/rt_computation/lfsx.ma".
  18
  19 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
  20
  21 axiom pippo: ∀h,o,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
  22              ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L & L ≡[h, o, V] L2.
  23
  24 (* Advanced properties ******************************************************)
  25
  26 lemma lfsx_lfdeq_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
  27                         ∀L2. L1 ≡[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
  28 #h #o #G #L1 #T #H @(lfsx_ind … H) -L1
  29 #L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
  30 #L #HL2 #HnL2 elim (lfdeq_lfpx_trans … HL2 … HL12) -HL2
  31 /4 width=5 by lfdeq_repl/
  32 qed-.
  33
  34 (* Advanced forward lemmas **************************************************)
  35
  36 (* Basic_2A1: was: lsx_fwd_bind_sn *)
  37 lemma lfsx_fwd_bind_sn: ∀h,o,p,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
  38                         G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄.
  39 #h #o #p #I #G #L #V #T #H @(lfsx_ind … H) -L
  40 #L1 #_ #IHL1 @lfsx_intro
  41 #L2 #H #HnL12 elim (pippo … o p I … T H) -H
  42 /6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_sn/
  43 qed-.
  44 (*
  45 lemma lfsx_fwd_flat_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
  46                        G ⊢ ⬈*[h, o, V, l] L.
  47 #h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
  48 #L1 #_ #IHL1 @lfsx_intro
  49 #L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_sn/
  50 qed-.
  51
  52 lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
  53                        G ⊢ ⬈*[h, o, T, l] L.
  54 #h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
  55 #L1 #_ #IHL1 @lfsx_intro
  56 #L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_dx/
  57 qed-.
  58
  59 lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ②{I}V.T, l] L →
  60                        G ⊢ ⬈*[h, o, V, l] L.
  61 #h #o * /2 width=4 by lfsx_fwd_bind_sn, lfsx_fwd_flat_sn/
  62 qed-.
  63
  64 (* Basic inversion lemmas ***************************************************)
  65
  66 lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
  67                     G ⊢ ⬈*[h, o, V, l] L ∧ G ⊢ ⬈*[h, o, T, l] L.
  68 /3 width=3 by lfsx_fwd_flat_sn, lfsx_fwd_flat_dx, conj/ qed-.
  69 *)