matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_length.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_length.ma".
  16 include "basic_2/rt_transition/rpx.ma".
  17
  18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
  19
  20 (* Forward lemmas with length for local environments ************************)
  21
  22 lemma rpx_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → |L1| = |L2|.
  23 /2 width=3 by rex_fwd_length/ qed-.
  24
  25 (* Inversion lemmas with length for local environments **********************)
  26
  27 lemma rpx_inv_zero_length: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
  28                            ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
  29                             | ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
  30                                                ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
  31                                                Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
  32                             | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
  33 /2 width=1 by rex_inv_zero_length/ qed-.