(* *)
(**************************************************************************)
-include "ground_2/xoa/ex_3_2.ma".
include "ground_2/xoa/ex_6_8.ma".
-include "ground_2/steps/rtc_isrt.ma".
+include "ground_2/steps/rtc.ma".
(* RT-TRANSITION COUNTER ****************************************************)
* #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2 * #ri3 #rs3 #ti3 #ts3
<plus_rew //
qed.
-
-(* Properties with test for constrained rt-transition counter ***************)
-
-lemma isrt_plus: ān1,n2,c1,c2. ššā¦n1,c1ā¦ ā ššā¦n2,c2ā¦ ā ššā¦n1+n2,c1+c2ā¦.
-#n1 #n2 #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct
-/2 width=3 by ex1_2_intro/
-qed.
-
-lemma isrt_plus_O1: ān,c1,c2. ššā¦0,c1ā¦ ā ššā¦n,c2ā¦ ā ššā¦n,c1+c2ā¦.
-/2 width=1 by isrt_plus/ qed.
-
-lemma isrt_plus_O2: ān,c1,c2. ššā¦n,c1ā¦ ā ššā¦0,c2ā¦ ā ššā¦n,c1+c2ā¦.
-#n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by isrt_plus/
-qed.
-
-lemma isrt_succ: ān,c. ššā¦n,cā¦ ā ššā¦ān,c+ššā¦.
-/2 width=1 by isrt_plus/ qed.
-
-(* Inversion properties with test for constrained rt-transition counter *****)
-
-lemma isrt_inv_plus: ān,c1,c2. ššā¦n,c1 + c2ā¦ ā
- āān1,n2. ššā¦n1,c1ā¦ & ššā¦n2,c2ā¦ & n1 + n2 = n.
-#n #c1 #c2 * #ri #rs #H
-elim (plus_inv_dx ā¦ H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2 #H3 #H4
-elim (plus_inv_O3 ā¦ H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/
-qed-.
-
-lemma isrt_inv_plus_O_dx: ān,c1,c2. ššā¦n,c1 + c2ā¦ ā ššā¦0,c2ā¦ ā ššā¦n,c1ā¦.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj ā¦ Hn2 H2) -c2 #H destruct //
-qed-.
-
-lemma isrt_inv_plus_SO_dx: ān,c1,c2. ššā¦n,c1 + c2ā¦ ā ššā¦1,c2ā¦ ā
- āām. ššā¦m,c1ā¦ & n = ām.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj ā¦ Hn2 H2) -c2 #H destruct
-/2 width=3 by ex2_intro/
-qed-.