+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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_plus.ma".
-include "ground/steps/rtc_ist.ma".
-
-(* RT-TRANSITION COUNTER ****************************************************)
-
-(* Properties with test for t-transition counter ****************************)
-
-lemma ist_plus: ān1,n2,c1,c2. šāŖn1,c1ā« ā šāŖn2,c2ā« ā šāŖn1+n2,c1+c2ā«.
-#n1 #n2 #c1 #c2 #H1 #H2 destruct //
-qed.
-
-lemma ist_plus_O1: ān,c1,c2. šāŖ0,c1ā« ā šāŖn,c2ā« ā šāŖn,c1+c2ā«.
-/2 width=1 by ist_plus/ qed.
-
-lemma ist_plus_O2: ān,c1,c2. šāŖn,c1ā« ā šāŖ0,c2ā« ā šāŖn,c1+c2ā«.
-#n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by ist_plus/
-qed.
-
-lemma ist_succ: ān,c. šāŖn,cā« ā šāŖān,c+ššā«.
-/2 width=1 by ist_plus/ qed.
-
-(* Inversion properties with test for constrained rt-transition counter *****)
-
-lemma ist_inv_plus:
- ān,c1,c2. šāŖn,c1 + c2ā« ā
- āān1,n2. šāŖn1,c1ā« & šāŖn2,c2ā« & n1 + n2 = n.
-#n #c1 #c2 #H
-elim (plus_inv_dx ā¦ H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct
-elim (plus_inv_O3 ā¦ H1) -H1 #H11 #H12 destruct
-elim (plus_inv_O3 ā¦ H2) -H2 #H21 #H22 destruct
-elim (plus_inv_O3 ā¦ H3) -H3 #H31 #H32 destruct
-/3 width=5 by ex3_2_intro/
-qed-.
-
-lemma ist_inv_plus_O_dx: ān,c1,c2. šāŖn,c1 + c2ā« ā šāŖ0,c2ā« ā šāŖn,c1ā«.
-#n #c1 #c2 #H #H2
-elim (ist_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
-qed-.
-
-lemma ist_inv_plus_SO_dx:
- ān,c1,c2. šāŖn,c1 + c2ā« ā šāŖ1,c2ā« ā
- āām. šāŖm,c1ā« & n = ām.
-#n #c1 #c2 #H #H2 destruct
-elim (ist_inv_plus ā¦ H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma ist_inv_plus_10_dx: ān,c. šāŖn,c+ššā« ā ā„.
-#n #c #H
-elim (ist_inv_plus ā¦ H) -H #n1 #n2 #_ #H #_
-/2 width=2 by ist_inv_10/
-qed-.