-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "ground/xoa/ex_3_2.ma".
-include "ground/steps/rtc_max.ma".
-include "ground/steps/rtc_isrt.ma".
-
-(* RT-TRANSITION COUNTER ****************************************************)
-
-(* Properties with test for constrained rt-transition counter ***************)
-
-lemma isrt_max: βn1,n2,c1,c2. ππβͺn1,c1β« β ππβͺn2,c2β« β ππβͺn1β¨n2,c1β¨c2β«.
-#n1 #n2 #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct
-/2 width=3 by ex1_2_intro/
-qed.
-
-lemma isrt_max_O1: βn,c1,c2. ππβͺ0,c1β« β ππβͺn,c2β« β ππβͺn,c1β¨c2β«.
-/2 width=1 by isrt_max/ qed.
-
-lemma isrt_max_O2: βn,c1,c2. ππβͺn,c1β« β ππβͺ0,c2β« β ππβͺn,c1β¨c2β«.
-#n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by isrt_max/
-qed.
-
-lemma isrt_max_idem1: βn,c1,c2. ππβͺn,c1β« β ππβͺn,c2β« β ππβͺn,c1β¨c2β«.
-#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: βn,c1,c2. ππβͺn,c1 β¨ c2β« β
- ββn1,n2. ππβͺn1,c1β« & ππβͺn2,c2β« & (n1 β¨ n2) = n.
-#n #c1 #c2 * #ri #rs #H
-elim (max_inv_dx β¦ H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2 #H3 #H4
-elim (max_inv_O3 β¦ H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/
-qed-.
-
-lemma isrt_O_inv_max: βc1,c2. ππβͺ0,c1 β¨ c2β« β β§β§ ππβͺ0,c1β« & ππβͺ0,c2β«.
-#c1 #c2 #H
-elim (isrt_inv_max β¦ H) -H #n1 #n2 #Hn1 #Hn2 #H
-elim (max_inv_O3 β¦ H) -H #H1 #H2 destruct
-/2 width=1 by conj/
-qed-.
-
-lemma isrt_inv_max_O_dx: βn,c1,c2. ππβͺn,c1 β¨ c2β« β ππβͺ0,c2β« β ππβͺn,c1β«.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_max β¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj β¦ Hn2 H2) -c2 #H destruct //
-qed-.
-
-lemma isrt_inv_max_eq_t: βn,c1,c2. ππβͺn,c1 β¨ c2β« β rtc_eq_t c1 c2 β
- β§β§ ππβͺn,c1β« & ππβͺn,c2β«.
-#n #c1 #c2 #H #Hc12
-elim (isrt_inv_max β¦ H) -H #n1 #n2 #Hc1 #Hc2 #H destruct
-lapply (isrt_eq_t_trans β¦ Hc1 β¦ Hc12) -Hc12 #H
-<(isrt_inj β¦ H β¦ Hc2) -Hc2
-<idempotent_max /2 width=1 by conj/
-qed-.