matita/matita/contribs/lambdadelta/basic_2A/etc/snta/lsubsn_cpcs.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/equivalence/cpcs_cpcs.ma".
  16 include "basic_2/dynamic/lsubsn.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE TYPE ASSIGNMENT *******)
  19
  20 (* Properties on context-sensitive parallel equivalence for terms ***********)
  21
  22 lemma cpr_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
  23                         ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
  24 /3 width=5 by lsubsn_fwd_lsubs2, cpr_lsubs_trans/ qed-.
  25
  26 lemma cprs_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
  27                          ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
  28 /3 width=5 by lsubsn_fwd_lsubs2, cprs_lsubs_trans/ qed-.
  29
  30 lemma cpcs_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
  31                          ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
  32 /3 width=5 by lsubsn_fwd_lsubs2, cpcs_lsubs_trans/ qed-.