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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 *)
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15 include "ground/xoa/ex_6_8.ma".
16 include "ground/arith/nat_max.ma".
17 include "ground/counters/rtc.ma".
19 (* MAXIMUM FOR RT-TRANSITION COUNTERS ***************************************)
21 definition rtc_max (c1:rtc) (c2:rtc): rtc ≝
23 [ mk_rtc ri1 rs1 ti1 ts1 ⇒
25 [ mk_rtc ri2 rs2 ti2 ts2 ⇒ 〈ri1∨ri2,rs1∨rs2,ti1∨ti2,ts1∨ts2〉
30 "maximum (rt-transition counters)"
31 'or c1 c2 = (rtc_max c1 c2).
33 (* Basic constructions ******************************************************)
36 lemma rtc_max_unfold (ri1) (ri2) (rs1) (rs2) (ti1) (ti2) (ts1) (ts2):
37 〈ri1∨ri2,rs1∨rs2,ti1∨ti2,ts1∨ts2〉 =
38 (〈ri1,rs1,ti1,ts1〉 ∨ 〈ri2,rs2,ti2,ts2〉).
41 lemma rtc_max_zz_dx (c): c = (c ∨ 𝟘𝟘).
42 * #ri #rs #ti #ts <rtc_max_unfold //
45 lemma rtc_max_idem (c): c = (c ∨ c).
46 * #ri #rs #ti #ts <rtc_max_unfold //
49 (* Basic inversions *********************************************************)
51 lemma rtc_max_inv_dx (ri) (rs) (ti) (ts) (c1) (c2):
52 〈ri,rs,ti,ts〉 = (c1 ∨ c2) →
53 ∃∃ri1,rs1,ti1,ts1,ri2,rs2,ti2,ts2.
54 (ri1∨ri2) = ri & (rs1∨rs2) = rs & (ti1∨ti2) = ti & (ts1∨ts2) = ts &
55 〈ri1,rs1,ti1,ts1〉 = c1 & 〈ri2,rs2,ti2,ts2〉 = c2.
56 #ri #rs #ti #ts * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2
57 <rtc_max_unfold #H destruct /2 width=14 by ex6_8_intro/
60 (* Main constructions *******************************************************)
62 theorem rtc_max_assoc: associative … rtc_max.
63 * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2 * #ri3 #rs3 #ti3 #ts3
64 <rtc_max_unfold <rtc_max_unfold //