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 *)
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15 include "ground/xoa/ex_6_8.ma".
16 include "ground/steps/rtc.ma".
18 (* RT-TRANSITION COUNTER ****************************************************)
20 definition max (c1:rtc) (c2:rtc): rtc ≝ match c1 with [
21 mk_rtc ri1 rs1 ti1 ts1 ⇒ match c2 with [
22 mk_rtc ri2 rs2 ti2 ts2 ⇒ 〈ri1∨ri2,rs1∨rs2,ti1∨ti2,ts1∨ts2〉
26 interpretation "maximum (rtc)"
27 'or c1 c2 = (max c1 c2).
29 (* Basic properties *********************************************************)
31 lemma max_rew: ∀ri1,ri2,rs1,rs2,ti1,ti2,ts1,ts2.
32 〈ri1∨ri2,rs1∨rs2,ti1∨ti2,ts1∨ts2〉 =
33 (〈ri1,rs1,ti1,ts1〉 ∨ 〈ri2,rs2,ti2,ts2〉).
36 lemma max_O_dx: ∀c. c = (c ∨ 𝟘𝟘).
37 * #ri #rs #ti #ts <max_rew //
40 lemma max_idem: ∀c. c = (c ∨ c).
41 * #ri #rs #ti #ts <max_rew //
44 (* Basic inversion properties ***********************************************)
46 lemma max_inv_dx: ∀ri,rs,ti,ts,c1,c2. 〈ri,rs,ti,ts〉 = (c1 ∨ c2) →
47 ∃∃ri1,rs1,ti1,ts1,ri2,rs2,ti2,ts2.
48 (ri1∨ri2) = ri & (rs1∨rs2) = rs & (ti1∨ti2) = ti & (ts1∨ts2) = ts &
49 〈ri1,rs1,ti1,ts1〉 = c1 & 〈ri2,rs2,ti2,ts2〉 = c2.
50 #ri #rs #ti #ts * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2
51 <max_rew #H destruct /2 width=14 by ex6_8_intro/
54 (* Main Properties **********************************************************)
56 theorem max_assoc: associative … max.
57 * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2 * #ri3 #rs3 #ti3 #ts3