matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.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 "ground_2/steps/rtc_shift.ma".
  16 include "ground_2/steps/rtc_ist.ma".
  17
  18 (* RT-TRANSITION COUNTER ****************************************************)
  19
  20 (* Properties with test for t-transition counter ****************************)
  21
  22 lemma ist_zero_shift: ∀c. 𝐓⦃0,c⦄ → 𝐓⦃0,↕*c⦄.
  23 #c #H destruct //
  24 qed.
  25
  26 (* Inversion properties with test for t-transition counter ******************)
  27
  28 lemma ist_inv_shift: ∀n,c. 𝐓⦃n,↕*c⦄ → ∧∧ 𝐓⦃0,c⦄ & 0 = n.
  29 #n #c #H
  30 elim (shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #H1 #_ #H2 #H3 #H4 destruct
  31 elim (max_inv_O3 … H1) -H1 #H11 #H12 destruct
  32 elim (max_inv_O3 … H2) -H2 #H21 #H22 destruct
  33 /2 width=1 by conj/
  34 qed-.
  35
  36 lemma ist_inv_zero_shift: ∀c. 𝐓⦃0,↕*c⦄ → 𝐓⦃0,c⦄.
  37 #c #H elim (ist_inv_shift … H) -H //
  38 qed-.