matita/matita/contribs/lambdadelta/basic_2/computation/csx_fpbs.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/fpbs.ma".
  16 include "basic_2/computation/csx_lpx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma csx_fpb_conf: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  23                     ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
  24 #h #g #G1 #L1 #T1 #HT1 #G2 #L2 #T2 *
  25 /2 width=5 by csx_cpx_trans, csx_fquq_conf, csx_lpx_conf/
  26 qed-.
  27
  28 lemma csx_fpbs_conf: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  29                      ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬊*[h, g] T2.
  30 #h #g #G1 #L1 #T1 #HT1 #G2 #L2 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
  31 /2 width=5 by csx_fpb_conf/
  32 qed-.
  33
  34 lemma csx_lpxs_conf: ∀h,g,G,L1. ∀T:term. ⦃G, L1⦄ ⊢ ⬊*[h, g] T →
  35                      ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
  36 /3 width=5 by csx_fpbs_conf, lpxs_fpbs/
  37 qed-.