matita/matita/contribs/lambdadelta/basic_2/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/computation/csx_aaa.ma".
  16 include "basic_2/computation/fsb_csx.ma".
  17
  18 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 (* Note: this is the "big tree" theorem ("small step" version) *)
  23 theorem aaa_fsb: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  24 /3 width=2 by aaa_csx, csx_fsb/ qed.
  25
  26 (* Note: this is the "big tree" theorem ("big step" version) *)
  27 theorem aaa_fsba: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⦥⦥[h, g] T.
  28 /3 width=2 by fsb_fsba, aaa_fsb/ qed.
  29
  30 (* Advanced eliminators on atomica arity assignment for terms ***************)
  31 (*
  32 fact aaa_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
  33                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
  34                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  35                                  R G1 L1 T1
  36                     ) →
  37                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
  38 #h #g #R #IH #G #L #T #H @(csx_ind_fpbu … H) -G -L -T
  39 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
  40 #G2 #L2 #T2 #H12 @IH1 //
  41 *)