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_2/steps/rtc_plus.ma".
16 include "ground_2/steps/rtc_ist.ma".
18 (* RT-TRANSITION COUNTER ****************************************************)
20 (* Properties with test for t-transition counter ****************************)
22 lemma ist_plus: ān1,n2,c1,c2. šā¦n1,c1ā¦ ā šā¦n2,c2ā¦ ā šā¦n1+n2,c1+c2ā¦.
23 #n1 #n2 #c1 #c2 #H1 #H2 destruct //
26 lemma ist_plus_O1: ān,c1,c2. šā¦0,c1ā¦ ā šā¦n,c2ā¦ ā šā¦n,c1+c2ā¦.
27 /2 width=1 by ist_plus/ qed.
29 lemma ist_plus_O2: ān,c1,c2. šā¦n,c1ā¦ ā šā¦0,c2ā¦ ā šā¦n,c1+c2ā¦.
30 #n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by ist_plus/
33 lemma ist_succ: ān,c. šā¦n,cā¦ ā šā¦ān,c+ššā¦.
34 /2 width=1 by ist_plus/ qed.
36 (* Inversion properties with test for constrained rt-transition counter *****)
39 ān,c1,c2. šā¦n,c1 + c2ā¦ ā
40 āān1,n2. šā¦n1,c1ā¦ & šā¦n2,c2ā¦ & n1 + n2 = n.
42 elim (plus_inv_dx ā¦ H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct
43 elim (plus_inv_O3 ā¦ H1) -H1 #H11 #H12 destruct
44 elim (plus_inv_O3 ā¦ H2) -H2 #H21 #H22 destruct
45 elim (plus_inv_O3 ā¦ H3) -H3 #H31 #H32 destruct
46 /3 width=5 by ex3_2_intro/
49 lemma ist_inv_plus_O_dx: ān,c1,c2. šā¦n,c1 + c2ā¦ ā šā¦0,c2ā¦ ā šā¦n,c1ā¦.
51 elim (ist_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
54 lemma ist_inv_plus_SO_dx:
55 ān,c1,c2. šā¦n,c1 + c2ā¦ ā šā¦1,c2ā¦ ā
56 āām. šā¦m,c1ā¦ & n = ām.
57 #n #c1 #c2 #H #H2 destruct
58 elim (ist_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
59 /2 width=3 by ex2_intro/
62 lemma ist_inv_plus_10_dx: ān,c. šā¦n,c+ššā¦ ā ā„.
64 elim (ist_inv_plus ā¦ H) -H #n1 #n2 #_ #H #_
65 /2 width=2 by ist_inv_10/