1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "ground/notation/relations/predicate_t_2.ma".
16 include "ground/counters/rtc.ma".
18 (* T-TRANSITION COUNTERS ****************************************************)
20 definition rtc_ist: relation2 nat rtc ≝
21 λts,c. 〈𝟎,𝟎,𝟎,ts〉 = c.
24 "construction (t-transition counters)"
25 'PredicateT ts c = (rtc_ist ts c).
27 (* Basic constructions ******************************************************)
29 lemma rtc_ist_zz: 𝐓❨𝟎,𝟘𝟘❩.
32 lemma rtc_ist_zu: 𝐓❨𝟏,𝟘𝟙❩.
35 (* Basic inversions *********************************************************)
37 lemma rtc_ist_inv_zz (n): 𝐓❨n,𝟘𝟘❩ → 𝟎 = n.
41 lemma rtc_ist_inv_zu (n): 𝐓❨n,𝟘𝟙❩ → ninj (𝟏) = n.
45 lemma rtc_ist_inv_uz (n): 𝐓❨n,𝟙𝟘❩ → ⊥.
49 (* Main inversions **********************************************************)
51 theorem rtc_ist_inj (n1) (n2) (c): 𝐓❨n1,c❩ → 𝐓❨n2,c❩ → n1 = n2.
52 #n1 #n2 #c #H1 #H2 destruct //
55 theorem rtc_ist_mono (n) (c1) (c2): 𝐓❨n,c1❩ → 𝐓❨n,c2❩ → c1 = c2.
56 #n #c1 #c2 #H1 #H2 destruct //