matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.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.ma".
  17
  18 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  19
  20 (* Advanced propreties ******************************************************)
  21
  22 lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  23 #h #g #G #L #T #H @(csx_ind_fpbc … H) -T /3 width=1 by fsb_intro/
  24 qed.
  25
  26 (* Main properties **********************************************************)
  27
  28 (* Note: this is the "big tree" theorem ("small step" version) *)
  29 theorem aaa_fsb: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  30 /3 width=2 by aaa_csx, csx_fsb/ qed.