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:                                           *)
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   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/rpx_fsle.ma".
  17 include "basic_2/rt_transition/lpx.ma".
  18
  19 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
  20
  21 (* Properties with syntactic equivalence for referred local environments ****)
  22
  23 lemma fleq_rpx (h) (G): ∀L1,L2,T. L1 ≡[T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
  24 /2 width=1 by req_fwd_rex/ qed.
  25
  26 (* Properties with unbound parallel rt-transition for full local envs *******)
  27
  28 lemma lpx_rpx: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
  29 /2 width=1 by rex_lex/ qed.
  30
  31 (* Inversion lemmas with unbound parallel rt-transition for full local envs *)
  32
  33 lemma rpx_inv_lpx_req: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 →
  34                        ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h] L & L ≡[T] L2.
  35 /3 width=3 by rpx_fsge_comp, rex_inv_lex_req/ qed-.