#n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by isrt_max/
qed.
+lemma isrt_max_idem1: โn,c1,c2. ๐๐โฆn, c1โฆ โ ๐๐โฆn, c2โฆ โ ๐๐โฆn, c1โจc2โฆ.
+#n #c1 #c2 #H1 #H2 >(idempotent_max n) /2 width=1 by isrt_max/
+qed.
+
(* Inversion properties with test for constrained rt-transition counter *****)
lemma isrt_inv_max: โn,c1,c2. ๐๐โฆn, c1 โจ c2โฆ โ
elim (max_inv_O3 โฆ H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/
qed-.
+lemma isrt_O_inv_max: โc1,c2. ๐๐โฆ0, c1 โจ c2โฆ โ โงโง ๐๐โฆ0, c1โฆ & ๐๐โฆ0, c2โฆ.
+#c1 #c2 #H
+elim (isrt_inv_max โฆ H) -H #n1 #n2 #Hn1 #Hn2 #H
+elim (max_inv_O3 โฆ H) -H #H1 #H2 destruct
+/2 width=1 by conj/
+qed-.
+
lemma isrt_inv_max_O_dx: โn,c1,c2. ๐๐โฆn, c1 โจ c2โฆ โ ๐๐โฆ0, c2โฆ โ ๐๐โฆn, c1โฆ.
#n #c1 #c2 #H #H2
elim (isrt_inv_max โฆ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_mono โฆ Hn2 H2) -c2 #H destruct //
+lapply (isrt_inj โฆ Hn2 H2) -c2 #H destruct //
qed-.
(* Properties with shift ****************************************************)
-lemma max_shift: รข\88\80c1,c2. ((รข\86\93c1) รข\88ยจ (รข\86\93c2)) = รข\86\93(c1โจc2).
+lemma max_shift: รข\88\80c1,c2. ((รข\86\95*c1) รข\88ยจ (รข\86\95*c2)) = รข\86\95*(c1โจc2).
* #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2
<shift_rew <shift_rew <shift_rew <max_rew //
qed.