matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_lpx.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 "static_2/static/rex_lex.ma".
  16 include "basic_2/rt_transition/cpx_req.ma".
  17 include "basic_2/rt_transition/lpx.ma".
  18
  19 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
  20
  21 (* Properties with syntactic equivalence for referred local environments ****)
  22
  23 lemma req_rpx (G) (T):
  24       ∀L1,L2. L1 ≡[T] L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
  25 /2 width=1 by req_fwd_rex/ qed.
  26
  27 (* Properties with extended rt-transition for full local envs ***************)
  28
  29 lemma lpx_rpx (G) (T):
  30       ∀L1,L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
  31 /2 width=1 by rex_lex/ qed.
  32
  33 (* Inversion lemmas with extended rt-transition for full local envs *********)
  34
  35 lemma rpx_inv_req_lpx (G) (T):
  36       ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
  37       ∃∃L. L1 ≡[T] L & ❪G,L❫ ⊢ ⬈ L2.
  38 /4 width=13 by cpx_req_conf, rex_inv_req_lex, rex_conf1_next/ qed-.
  39
  40 (* Forward lemmas with extended rt-transition for full local envs ***********)
  41
  42 lemma rpx_fwd_lpx_req (G) (T):
  43       ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
  44       ∃∃L. ❪G,L1❫ ⊢ ⬈ L & L ≡[T] L2.
  45 /3 width=3 by rpx_fsge_comp, rex_fwd_lex_req/ qed-.