matita/matita/contribs/lambdadelta/ground/counters/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/counters/rtc_shift.ma".
  16 include "ground/counters/rtc_ist.ma".
  17
  18 (* T-BOUND RT-TRANSITION COUNTERS *******************************************)
  19
  20 (* Constructions with rtc_shift *********************************************)
  21
  22 lemma rtc_ist_zero_shift (c): 𝐓❪𝟎,c❫ → 𝐓❪𝟎,↕*c❫.
  23 #c #H destruct //
  24 qed.
  25
  26 (* Inversions with rtc_shift ************************************************)
  27
  28 lemma rtc_ist_inv_shift (n) (c): 𝐓❪n,↕*c❫ → ∧∧ 𝐓❪𝟎,c❫ & 𝟎 = n.
  29 #n #c #H
  30 elim (rtc_shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #H1 #_ #H2 #H3 #H4 destruct
  31 elim (eq_inv_nmax_zero … H1) -H1 #H11 #H12 destruct
  32 elim (eq_inv_nmax_zero … H2) -H2 #H21 #H22 destruct
  33 /2 width=1 by conj/
  34 qed-.
  35
  36 lemma rtc_ist_inv_zero_shift (c): 𝐓❪𝟎,↕*c❫ → 𝐓❪𝟎,c❫.
  37 #c #H elim (rtc_ist_inv_shift … H) -H //
  38 qed-.