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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/computation/lsx_csx.ma".
  16 include "basic_2/computation/fsb_alt.ma".
  17
  18 axiom lsx_fqup_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
  19                      G1 ⊢ ⋕⬊*[h, g, T1, 0] L1 → G2 ⊢ ⋕⬊*[h, g, T2, 0] L2.
  20
  21 axiom fqup_lpxs_trans_nlleq: ∀h,g,G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ →
  22                              ∀L2. ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 → (K2 ⋕[T2, 0] L2 →⊥) →
  23                              ∃∃L1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 &
  24                                    K1 ⋕[T1, 0] L1 → ⊥ & ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
  25
  26 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  27
  28 (* Advanced propreties on context-senstive extended bormalizing terms *******)
  29
  30 lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  31 #h #g #G1 #L1 #T1 #H @(csx_ind_alt … H) -T1
  32 #T1 #HT1 @(lsx_ind h g G1 T1 0 … L1) /2 width=1 by csx_lsx/ -L1
  33 #L1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
  34 #G1 #L1 #T1 #IHu #H1 #IHl #IHc @fsb_intro
  35 #G2 #L2 #T2 * -G2 -L2 -T2
  36 [ #G2 #L2 #T2 #H12 @IHu -IHu /2 width=5 by lsx_fqup_conf/ -H1 [| -IHl ]
  37   [ #L0 #HL20 #HnL20 #_ elim (fqup_lpxs_trans_nlleq … H12 … HL20 HnL20) -L2
  38     /6 width=5 by fsb_fpbs_trans, lpxs_fpbs, fqup_fpbs, lpxs_cpxs_trans/
  39   | #T0 #HT20 #HnT20 elim (fqup_cpxs_trans_neq … H12 … HT20 HnT20) -T2
  40     /4 width=5 by fsb_fpbs_trans, fqup_fpbs/
  41   ]
  42 | -H1 -IHu -IHl /3 width=1 by/
  43 | -H1 -IHu /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, lpxs_cpxs_trans/
  44 ]
  45 qed.
  46
  47 (* Advanced eliminators *****************************************************)
  48
  49 lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
  50                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  51                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  52                                 R G1 L1 T1
  53                     ) →
  54                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  55 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
  56
  57 lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
  58                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  59                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  60                                 R G1 L1 T1
  61                     ) →
  62                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  63 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.