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

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   2 (*       ___                                                              *)
   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/rt_computation/fpbg_fpbs.ma".
  16 include "basic_2/rt_computation/fsb_fdeq.ma".
  17
  18 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
  19
  20 (* Properties with parallel rst-computation for closures ********************)
  21
  22 lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
  23                       ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → ≥[h] 𝐒⦃G2, L2, T2⦄.
  24 #h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
  25 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
  26 elim (fpbs_inv_fpbg … H12) -H12
  27 [ -IH /2 width=5 by fsb_fdeq_trans/
  28 | -H1 * /2 width=5 by/
  29 ]
  30 qed-.
  31
  32 (* Properties with proper parallel rst-computation for closures *************)
  33
  34 lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
  35                          ∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄ → ≥[h] 𝐒⦃G2, L2, T2⦄
  36                       ) → ≥[h] 𝐒⦃G1, L1, T1⦄.
  37 /4 width=1 by fsb_intro, fpb_fpbg/ qed.
  38
  39 (* Eliminators with proper parallel rst-computation for closures ************)
  40
  41 lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
  42                          (∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
  43                                      (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
  44                                      Q G1 L1 T1
  45                          ) →
  46                          ∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
  47                          ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
  48 #h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
  49 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
  50 @IH1 -IH1
  51 [ -IH /2 width=5 by fsb_fpbs_trans/
  52 | -H1 #G0 #L0 #T0 #H10
  53   elim (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2
  54   /2 width=5 by/
  55 ]
  56 qed-.
  57
  58 lemma fsb_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
  59                     (∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
  60                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
  61                                 Q G1 L1 T1
  62                     ) →
  63                     ∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →  Q G1 L1 T1.
  64 #h #Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
  65 /3 width=1 by/
  66 qed-.
  67
  68 (* Inversion lemmas with proper parallel rst-computation for closures *******)
  69
  70 lemma fsb_fpbg_refl_false (h) (G) (L) (T):
  71                           ≥[h] 𝐒⦃G, L, T⦄ → ⦃G, L, T⦄ >[h] ⦃G, L, T⦄ → ⊥.
  72 #h #G #L #T #H
  73 @(fsb_ind_fpbg … H) -G -L -T #G1 #L1 #T1 #_ #IH #H
  74 /2 width=5 by/
  75 qed-.