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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  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/csx_aaa.ma".
  16 include "basic_2/rt_computation/fpbs_aaa.ma".
  17 include "basic_2/rt_computation/fpbs_fpb.ma".
  18 include "basic_2/rt_computation/fsb_csx.ma".
  19
  20 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
  21
  22 (* Main properties with atomic arity assignment for terms *******************)
  23
  24 theorem aaa_fsb: ∀h,G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ≥[h] 𝐒❪G,L,T❫.
  25 /3 width=2 by aaa_csx, csx_fsb/ qed.
  26
  27 (* Advanced eliminators with atomic arity assignment for terms **************)
  28
  29 fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
  30                       (∀G1,L1,T1,A. ❪G1,L1❫ ⊢ T1 ⁝ A →
  31                                     (∀G2,L2,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
  32                                     Q G1 L1 T1
  33                       ) →
  34                       ∀G,L,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
  35 #h #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
  36 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
  37 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
  38 /2 width=2 by fpb_fpbs/
  39 qed-.
  40
  41 lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
  42                    (∀G1,L1,T1,A. ❪G1,L1❫ ⊢ T1 ⁝ A →
  43                                  (∀G2,L2,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
  44                                  Q G1 L1 T1
  45                    ) →
  46                    ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
  47 /4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
  48
  49 fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
  50                        (∀G1,L1,T1,A. ❪G1,L1❫ ⊢ T1 ⁝ A →
  51                                      (∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
  52                                      Q G1 L1 T1
  53                        ) →
  54                        ∀G,L,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
  55 #h #Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
  56 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
  57 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
  58 /2 width=2 by fpbg_fwd_fpbs/
  59 qed-.
  60
  61 lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
  62                     (∀G1,L1,T1,A. ❪G1,L1❫ ⊢ T1 ⁝ A →
  63                                   (∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
  64                                   Q G1 L1 T1
  65                     ) →
  66                     ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
  67 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.