matita/matita/contribs/lambdadelta/ground/counters/rtc_ism_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_ism.ma".
  17
  18 (* T-BOUND RT-TRANSITION COUNTERS *******************************************)
  19
  20 (* Constructions with rtc_shift *********************************************)
  21
  22 lemma rtc_isr_shift (c):  𝐌❪𝟎,c❫ → 𝐌❪𝟎,↕*c❫.
  23 #c * #ri #rs #H destruct /2 width=3 by ex1_2_intro/
  24 qed.
  25
  26 (* Inversions with rtc_shift ************************************************)
  27
  28 lemma rtc_ism_inv_shift (n) (c): 𝐌❪n,↕*c❫ → ∧∧ 𝐌❪𝟎,c❫ & 𝟎 = n.
  29 #n #c * #ri #rs #H
  30 elim (rtc_shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
  31 elim (eq_inv_nmax_zero … H1) -H1 /3 width=3 by ex1_2_intro, conj/
  32 qed-.
  33
  34 lemma rtc_isr_inv_shift (c): 𝐌❪𝟎,↕*c❫ → 𝐌❪𝟎,c❫.
  35 #c #H elim (rtc_ism_inv_shift … H) -H //
  36 qed-.