matita/matita/contribs/lambdadelta/ground_2/steps/rtc_isrt_shift.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
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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 "ground_2/steps/rtc_shift.ma".
  16 include "ground_2/steps/rtc_isrt.ma".
  17
  18 (* RT-TRANSITION COUNTER ****************************************************)
  19
  20 (* Properties with test for costrained rt-transition counter ****************)
  21
  22 lemma isr_shift: ∀c. 𝐑𝐓❪0,c❫ → 𝐑𝐓❪0,↕*c❫.
  23 #c * #ri #rs #H destruct /2 width=3 by ex1_2_intro/
  24 qed.
  25
  26 (* Inversion properties with test for costrained rt-counter *****************)
  27
  28 lemma isrt_inv_shift: ∀n,c. 𝐑𝐓❪n,↕*c❫ → 𝐑𝐓❪0,c❫ ∧ 0 = n.
  29 #n #c * #ri #rs #H
  30 elim (shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
  31 elim (max_inv_O3 … H1) -H1 /3 width=3 by ex1_2_intro, conj/
  32 qed-.
  33
  34 lemma isr_inv_shift: ∀c. 𝐑𝐓❪0,↕*c❫ → 𝐑𝐓❪0,c❫.
  35 #c #H elim (isrt_inv_shift … H) -H //
  36 qed-.