matita/matita/contribs/lambdadelta/basic_2/etc/cpr/aaa_ltpss_sn.etc

   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/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/static/aaa_ltpss_dx.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties about sn parallel unfold **************************************)
  21
  22 lemma aaa_ltpss_sn_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
  23                          ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
  24 #L1 #T #A #HT #L2 #d #e #HL12
  25 lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
  26 @(TC_Conf3 … (λL,A. L ⊢ T ⁝ A) … HT ? HL12) /2 width=5/
  27 qed.
  28
  29 lemma aaa_ltpss_sn_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  30                               ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  31                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
  32 /3 width=5/ qed.
  33
  34 lemma aaa_ltpss_sn_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  35                              ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  36                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
  37 /3 width=5/ qed.