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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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11 (*        v         GNU General Public License Version 2                  *)
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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):  ๐Œโจ๐ŸŽ,cโฉ โ†’ ๐Œโจ๐ŸŽ,โ†•*cโฉ.
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): ๐Œโจn,โ†•*cโฉ โ†’ โˆงโˆง ๐Œโจ๐ŸŽ,cโฉ & ๐ŸŽ = n.
29 #n #c * #ri #rs #H
30 elim (rtc_shift_inv_dx โ€ฆ H) -H #rt0 #rs0 #ti0 #ts0 #_ #_ #H1 #H2 #H3
31 elim (eq_inv_nmax_zero โ€ฆ H1) -H1 /3 width=3 by ex1_2_intro, conj/
32 qed-.
33
34 lemma rtc_isr_inv_shift (c): ๐Œโจ๐ŸŽ,โ†•*cโฉ โ†’ ๐Œโจ๐ŸŽ,cโฉ.
35 #c #H elim (rtc_ism_inv_shift โ€ฆ H) -H //
36 qed-.