propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / counters / rtc_ism_shift.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/counters/rtc_ism_shift.ma b/matita/matita/contribs/lambdadelta/ground/counters/rtc_ism_shift.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/counters/rtc_shift.ma".
+include "ground/counters/rtc_ism.ma".
+
+(* T-BOUND RT-TRANSITION COUNTERS *******************************************)
+
+(* Constructions with rtc_shift *********************************************)
+
+lemma rtc_isr_shift (c):  𝐌❪𝟎,c❫ → 𝐌❪𝟎,↕*c❫.
+#c * #ri #rs #H destruct /2 width=3 by ex1_2_intro/
+qed.
+
+(* Inversions with rtc_shift ************************************************)
+
+lemma rtc_ism_inv_shift (n) (c): 𝐌❪n,↕*c❫ → ∧∧ 𝐌❪𝟎,c❫ & 𝟎 = n.
+#n #c * #ri #rs #H
+elim (rtc_shift_inv_dx … H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
+elim (eq_inv_nmax_zero … H1) -H1 /3 width=3 by ex1_2_intro, conj/
+qed-.
+
+lemma rtc_isr_inv_shift (c): 𝐌❪𝟎,↕*c❫ → 𝐌❪𝟎,c❫.
+#c #H elim (rtc_ism_inv_shift … H) -H //
+qed-.