From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Mon, 30 Sep 2019 18:12:31 +0000 (+0200)
Subject: update in ground_2 and basic_2
X-Git-Tag: make_still_working~230
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=b4f76b0d8fa0e5365fb48e91474febe200b647a7;p=helm.git
update in ground_2 and basic_2
+ initial support for t-transition (the core of inferred type assignment)
---
diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pty_6.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pty_6.ma
new file mode 100644
index 000000000..0fb47e92f
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pty_6.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦠term 46 G, break term 46 L ⦠⢠break term 46 T1 â¬[ break term 46 h, break term 46 n ] break term 46 T2 )"
+ non associative with precedence 45
+ for @{ 'PTy $h $n $G $L $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/ptystar_6.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/ptystar_6.ma
new file mode 100644
index 000000000..884303830
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/ptystar_6.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦠term 46 G, break term 46 L ⦠⢠break term 46 T1 â¬*[ break term 46 h, break term 46 n ] break term 46 T2 )"
+ non associative with precedence 45
+ for @{ 'PTyStar $h $n $G $L $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
new file mode 100644
index 000000000..0ccb505e6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
@@ -0,0 +1,95 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_2/steps/rtc_ist_shift.ma".
+include "ground_2/steps/rtc_ist_plus.ma".
+include "ground_2/steps/rtc_ist_max.ma".
+include "basic_2/notation/relations/pty_6.ma".
+include "basic_2/rt_transition/cpg.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
+
+definition cpt (h) (G) (L) (n): relation2 term term â
+ λT1,T2. ââc. ðâ¦n,c⦠& â¦G,L⦠⢠T1 â¬[eq â¦,c,h] T2.
+
+interpretation
+ "t-bound context-sensitive parallel t-transition (term)"
+ 'PTy h n G L T1 T2 = (cpt h G L n T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma cpt_ess (h) (G) (L):
+ âs. â¦G,L⦠⢠âs â¬[h,1] â(⫯[h]s).
+/2 width=3 by cpg_ess, ex2_intro/ qed.
+
+lemma cpt_delta (h) (n) (G) (K):
+ âV1,V2. â¦G,K⦠⢠V1 â¬[h,n] V2 â
+ âW2. â§*[1] V2 â W2 â â¦G,K.âV1⦠⢠#0 â¬[h,n] W2.
+#h #n #G #K #V1 #V2 *
+/3 width=5 by cpg_delta, ex2_intro/
+qed.
+
+lemma cpt_ell (h) (n) (G) (K):
+ âV1,V2. â¦G,K⦠⢠V1 â¬[h,n] V2 â
+ âW2. â§*[1] V2 â W2 â â¦G,K.âV1⦠⢠#0 â¬[h,ân] W2.
+#h #n #G #K #V1 #V2 *
+/3 width=5 by cpg_ell, ex2_intro, ist_succ/
+qed.
+
+lemma cpt_lref (h) (n) (G) (K):
+ âT,i. â¦G,K⦠⢠#i â¬[h,n] T â âU. â§*[1] T â U â
+ âI. â¦G,K.â{I}⦠⢠#âi â¬[h,n] U.
+#h #n #G #K #T #i *
+/3 width=5 by cpg_lref, ex2_intro/
+qed.
+
+lemma cpt_bind (h) (n) (G) (L):
+ âV1,V2. â¦G,L⦠⢠V1 â¬[h,0] V2 â âI,T1,T2. â¦G,L.â{I}V1⦠⢠T1 â¬[h,n] T2 â
+ âp. â¦G,L⦠⢠â{p,I}V1.T1 â¬[h,n] â{p,I}V2.T2.
+#h #n #G #L #V1 #V2 * #cV #HcV #HV12 #I #T1 #T2 *
+/3 width=5 by cpg_bind, ist_max_O1, ex2_intro/
+qed.
+
+lemma cpt_appl (h) (n) (G) (L):
+ âV1,V2. â¦G,L⦠⢠V1 â¬[h,0] V2 â
+ âT1,T2. â¦G,L⦠⢠T1 â¬[h,n] T2 â â¦G,L⦠⢠âV1.T1 â¬[h,n] âV2.T2.
+#h #n #G #L #V1 #V2 * #cV #HcV #HV12 #T1 #T2 *
+/3 width=5 by ist_max_O1, cpg_appl, ex2_intro/
+qed.
+
+lemma cpt_cast (h) (n) (G) (L):
+ âU1,U2. â¦G,L⦠⢠U1 â¬[h,n] U2 â
+ âT1,T2. â¦G,L⦠⢠T1 â¬[h,n] T2 â â¦G,L⦠⢠âU1.T1 â¬[h,n] âU2.T2.
+#h #n #G #L #U1 #U2 * #cU #HcU #HU12 #T1 #T2 *
+/3 width=6 by cpg_cast, ex2_intro/
+qed.
+
+lemma cpt_ee (h) (n) (G) (L):
+ âU1,U2. â¦G,L⦠⢠U1 â¬[h,n] U2 â âT. â¦G,L⦠⢠âU1.T â¬[h,ân] U2.
+#h #n #G #L #V1 #V2 *
+/3 width=3 by cpg_ee, ist_succ, ex2_intro/
+qed.
+
+(* Basic properties *********************************************************)
+
+lemma cpt_refl (h) (G) (L): reflexive ⦠(cpt h G L 0).
+/3 width=3 by cpg_refl, ex2_intro/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma cpt_sort (h) (G) (L):
+ ân. n ⤠1 â âs. â¦G,L⦠⢠âs â¬[h,n] â((next h)^n s).
+#h #G #L * //
+#n #H #s <(le_n_O_to_eq n) /2 width=1 by le_S_S_to_le/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_cpm.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_cpm.ma
new file mode 100644
index 000000000..c37ddc224
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_cpm.ma
@@ -0,0 +1,66 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "basic_2/rt_transition/cpm_drops.ma".
+include "basic_2/rt_transition/cpt_drops.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
+
+(* Properties with t-bound rt-transition for terms **************************)
+
+lemma cpm_cpt_cpr (h) (n) (G) (L):
+ âT1,T2. â¦G,L⦠⢠T1 â¡[n,h] T2 â
+ ââT0. â¦G,L⦠⢠T1 â¬[h,n] T0 & â¦G,L⦠⢠T0 â¡[h] T2.
+#h #n #G #L #T1 #T2 #H
+@(cpm_ind ⦠H) -n -G -L -T1 -T2
+[ #I #G #L /2 width=3 by ex2_intro/
+| #G #L #s /3 width=3 by cpm_sort, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #_ * #V0 #HV10 #HV02 #HVW2
+ elim (lifts_total V0 (ðâ´1âµ)) #W0 #HVW0
+ lapply (cpm_lifts_bi ⦠HV02 (â) ⦠(K.âV1) ⦠HVW0 ⦠HVW2) -HVW2
+ [ /3 width=1 by drops_refl, drops_drop/ ] -HV02 #HW02
+ /3 width=3 by cpt_delta, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #_ * #V0 #HV10 #HV02 #HVW2
+ elim (lifts_total V0 (ðâ´1âµ)) #W0 #HVW0
+ lapply (cpm_lifts_bi ⦠HV02 (â) ⦠(K.âV1) ⦠HVW0 ⦠HVW2) -HVW2
+ [ /3 width=1 by drops_refl, drops_drop/ ] -HV02 #HW02
+ /3 width=3 by cpt_ell, ex2_intro/
+| #n #I #G #K #T2 #U2 #i #_ * #T0 #HT0 #HT02 #HTU2
+ elim (lifts_total T0 (ðâ´1âµ)) #U0 #HTU0
+ lapply (cpm_lifts_bi ⦠HT02 (â) ⦠(K.â{I}) ⦠HTU0 ⦠HTU2) -HTU2
+ [ /3 width=1 by drops_refl, drops_drop/ ] -HT02 #HU02
+ /3 width=3 by cpt_lref, ex2_intro/
+| #n #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ * #T0 #HT10 #HT02
+ /3 width=5 by cpt_bind, cpm_bind, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ * #T0 #HT10 #HT02
+ /3 width=5 by cpt_appl, cpm_appl, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #_ #_ * #V0 #HV10 #HV02 * #T0 #HT10 #HT02
+ /3 width=5 by cpt_cast, cpm_cast, ex2_intro/
+| #n #G #L #V #U1 #T1 #T2 #HTU1 #_ * #T0 #HT10 #HT02
+ elim (cpt_lifts_sn ⦠HT10 (â) ⦠(L.âV) ⦠HTU1) -T1
+ [| /3 width=1 by drops_refl, drops_drop/ ] #U0 #HTU0 #HU10
+ /3 width=6 by cpt_bind, cpm_zeta, ex2_intro/
+| #n #G #L #U #T1 #T2 #_ * #T0 #HT10 #HT02
+| #n #G #L #U1 #U2 #T #_ * #U0 #HU10 #HU02
+ /3 width=3 by cpt_ee, ex2_intro/
+| #n #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ * #T0 #HT10 #HT02
+ /4 width=7 by cpt_appl, cpt_bind, cpm_beta, ex2_intro/
+| #n #p #G #L #V1 #V2 #V0 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ * #T0 #HT10 #HT02 #HV20
+ /4 width=9 by cpt_appl, cpt_bind, cpm_theta, ex2_intro/
+]
+
+(* Forward lemmas with t-bound rt-transition for terms **********************)
+
+lemma cpt_fwd_cpm (h) (n) (G) (L):
+ âT1,T2. â¦G,L⦠⢠T1 â¬[h,n] T2 â â¦G,L⦠⢠T1 â¡[n,h] T2.
\ No newline at end of file
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma
new file mode 100644
index 000000000..6447e51ae
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_drops.ma
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "basic_2/rt_transition/cpg_drops.ma".
+include "basic_2/rt_transition/cpt.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma cpt_lifts_sn (h) (n) (G):
+ d_liftable2_sn ⦠lifts (λL. cpt h G L n).
+#h #n #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
+elim (cpg_lifts_sn ⦠HT12 ⦠HLK ⦠HTU1) -K -T1
+/3 width=5 by ex2_intro/
+qed-.
+
+lemma cpt_lifts_bi (h) (n) (G):
+ d_liftable2_bi ⦠lifts (λL. cpt h G L n).
+#h #n #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
+qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+lemma cpt_inv_lifts_sn (h) (n) (G):
+ d_deliftable2_sn ⦠lifts (λL. cpt h G L n).
+#h #n #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
+elim (cpg_inv_lifts_sn ⦠HU12 ⦠HLK ⦠HTU1) -L -U1
+/3 width=5 by ex2_intro/
+qed-.
+
+lemma cpt_inv_lifts_bi (h) (n) (G):
+ d_deliftable2_bi ⦠lifts (λL. cpt h G L n).
+#h #n #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 62987557d..671bd5bae 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -92,6 +92,10 @@ table {
]
class "cyan"
[ { "rt-transition" * } {
+ [ { "context-sensitive parallel t-transition" * } {
+ [ [ "for terms" ] "cpt" + "( â¦?,?⦠⢠? â¬[?,?] ? )" "cpt_drops" + "cpt_cpm" * ]
+ }
+ ]
[ { "context-sensitive parallel r-transition" * } {
[ [ "normal form for terms" ] "cnr ( â¦?,?⦠⢠â¡[?] ðâ¦?⦠)" "cnr_simple" + "cnr_tdeq" + "cnr_drops" * ]
[ [ "for lenvs on all entries" ] "lpr" + "( â¦?,?⦠⢠â¡[?] ? )" "lpr_length" + "lpr_drops" + "lpr_fquq" + "lpr_aaa" + "lpr_lpx" + "lpr_lpr" * ]
diff --git a/matita/matita/contribs/lambdadelta/ground_2/notation/relations/istype_2.ma b/matita/matita/contribs/lambdadelta/ground_2/notation/relations/istype_2.ma
new file mode 100644
index 000000000..795d811ab
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/notation/relations/istype_2.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+(* GENERAL NOTATION USED BY THE FORMAL SYSTEM λδ ****************************)
+
+notation "hvbox( ð⦠term 46 n, break term 46 c ⦠)"
+ non associative with precedence 45
+ for @{ 'IsType $n $c }.
diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.ma
new file mode 100644
index 000000000..6b9b64681
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist.ma
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_2/notation/relations/istype_2.ma".
+include "ground_2/steps/rtc.ma".
+
+(* T-TRANSITION COUNTER *****************************************************)
+
+definition ist: relation2 nat rtc â
+ λts,c. â©0,0,0,ts⪠= c.
+
+interpretation "test for t-transition counter (rtc)"
+ 'IsType ts c = (ist ts c).
+
+(* Basic properties *********************************************************)
+
+lemma isr_00: ðâ¦0,ððâ¦.
+// qed.
+
+lemma ist_01: ðâ¦1,ððâ¦.
+// qed.
+
+(* Basic inversion properties ***********************************************)
+
+lemma ist_inv_00: ân. ðâ¦n,ðð⦠â 0 = n.
+#n #H destruct //
+qed-.
+
+lemma ist_inv_01: ân. ðâ¦n,ðð⦠â 1 = n.
+#n #H destruct //
+qed-.
+
+(* Main inversion properties ************************************************)
+
+theorem ist_inj: ân1,n2,c. ðâ¦n1,c⦠â ðâ¦n2,c⦠â n1 = n2.
+#n1 #n2 #c #H1 #H2 destruct //
+qed-.
+
+theorem ist_mono: ân,c1,c2. ðâ¦n,c1⦠â ðâ¦n,c2⦠â c1 = c2.
+#n #c1 #c2 #H1 #H2 destruct //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma
new file mode 100644
index 000000000..ba31b7faa
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma
@@ -0,0 +1,60 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_2/steps/rtc_max.ma".
+include "ground_2/steps/rtc_ist.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+(* Properties with test for t-transition counter ****************************)
+
+lemma ist_max: ân1,n2,c1,c2. ðâ¦n1,c1⦠â ðâ¦n2,c2⦠â ðâ¦n1â¨n2,c1â¨c2â¦.
+#n1 #n2 #c1 #c2 #H1 #H2 destruct //
+qed.
+
+lemma ist_max_O1: ân,c1,c2. ðâ¦0,c1⦠â ðâ¦n,c2⦠â ðâ¦n,c1â¨c2â¦.
+/2 width=1 by ist_max/ qed.
+
+lemma ist_max_O2: ân,c1,c2. ðâ¦n,c1⦠â ðâ¦0,c2⦠â ðâ¦n,c1â¨c2â¦.
+#n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by ist_max/
+qed.
+
+lemma ist_max_idem1: ân,c1,c2. ðâ¦n,c1⦠â ðâ¦n,c2⦠â ðâ¦n,c1â¨c2â¦.
+#n #c1 #c2 #H1 #H2 >(idempotent_max n) /2 width=1 by ist_max/
+qed.
+
+(* Inversion properties with test for t-transition counter ******************)
+
+lemma ist_inv_max:
+ ân,c1,c2. ðâ¦n,c1 ⨠c2⦠â
+ âân1,n2. ðâ¦n1,c1⦠& ðâ¦n2,c2⦠& (n1 ⨠n2) = n.
+#n #c1 #c2 #H
+elim (max_inv_dx ⦠H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct
+elim (max_inv_O3 ⦠H1) -H1 #H11 #H12 destruct
+elim (max_inv_O3 ⦠H2) -H2 #H21 #H22 destruct
+elim (max_inv_O3 ⦠H3) -H3 #H31 #H32 destruct
+/2 width=5 by ex3_2_intro/
+qed-.
+
+lemma ist_O_inv_max: âc1,c2. ðâ¦0,c1 ⨠c2⦠â â§â§ ðâ¦0,c1⦠& ðâ¦0,c2â¦.
+#c1 #c2 #H
+elim (ist_inv_max ⦠H) -H #n1 #n2 #Hn1 #Hn2 #H
+elim (max_inv_O3 ⦠H) -H #H1 #H2 destruct
+/2 width=1 by conj/
+qed-.
+
+lemma ist_inv_max_O_dx: ân,c1,c2. ðâ¦n,c1 ⨠c2⦠â ðâ¦0,c2⦠â ðâ¦n,c1â¦.
+#n #c1 #c2 #H #H2
+elim (ist_inv_max ⦠H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma
new file mode 100644
index 000000000..c17eec5b6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma
@@ -0,0 +1,60 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_2/steps/rtc_plus.ma".
+include "ground_2/steps/rtc_ist.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+(* Properties with test for t-transition counter ****************************)
+
+lemma ist_plus: ân1,n2,c1,c2. ðâ¦n1,c1⦠â ðâ¦n2,c2⦠â ðâ¦n1+n2,c1+c2â¦.
+#n1 #n2 #c1 #c2 #H1 #H2 destruct //
+qed.
+
+lemma ist_plus_O1: ân,c1,c2. ðâ¦0,c1⦠â ðâ¦n,c2⦠â ðâ¦n,c1+c2â¦.
+/2 width=1 by ist_plus/ qed.
+
+lemma ist_plus_O2: ân,c1,c2. ðâ¦n,c1⦠â ðâ¦0,c2⦠â ðâ¦n,c1+c2â¦.
+#n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by ist_plus/
+qed.
+
+lemma ist_succ: ân,c. ðâ¦n,c⦠â ðâ¦ân,c+ððâ¦.
+/2 width=1 by ist_plus/ qed.
+
+(* Inversion properties with test for constrained rt-transition counter *****)
+
+lemma ist_inv_plus:
+ ân,c1,c2. ðâ¦n,c1 + c2⦠â
+ âân1,n2. ðâ¦n1,c1⦠& ðâ¦n2,c2⦠& n1 + n2 = n.
+#n #c1 #c2 #H
+elim (plus_inv_dx ⦠H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct
+elim (plus_inv_O3 ⦠H1) -H1 #H11 #H12 destruct
+elim (plus_inv_O3 ⦠H2) -H2 #H21 #H22 destruct
+elim (plus_inv_O3 ⦠H3) -H3 #H31 #H32 destruct
+/3 width=5 by ex3_2_intro/
+qed-.
+
+lemma ist_inv_plus_O_dx: ân,c1,c2. ðâ¦n,c1 + c2⦠â ðâ¦0,c2⦠â ðâ¦n,c1â¦.
+#n #c1 #c2 #H #H2
+elim (ist_inv_plus ⦠H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
+qed-.
+
+lemma ist_inv_plus_SO_dx:
+ ân,c1,c2. ðâ¦n,c1 + c2⦠â ðâ¦1,c2⦠â
+ ââm. ðâ¦m,c1⦠& n = âm.
+#n #c1 #c2 #H #H2 destruct
+elim (ist_inv_plus ⦠H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
+/2 width=3 by ex2_intro/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.ma
new file mode 100644
index 000000000..99ad5a092
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_shift.ma
@@ -0,0 +1,38 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_2/steps/rtc_shift.ma".
+include "ground_2/steps/rtc_ist.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+(* Properties with test for t-transition counter ****************************)
+
+lemma ist_zero_shift: âc. ðâ¦0,c⦠â ðâ¦0,â*câ¦.
+#c #H destruct //
+qed.
+
+(* Inversion properties with test for t-transition counter ******************)
+
+lemma ist_inv_shift: ân,c. ðâ¦n,â*c⦠â â§â§ ðâ¦0,c⦠& 0 = n.
+#n #c #H
+elim (shift_inv_dx ⦠H) -H #rt0 #rs0 #ti0 #ts0 #H1 #_ #H2 #H3 #H4 destruct
+elim (max_inv_O3 ⦠H1) -H1 #H11 #H12 destruct
+elim (max_inv_O3 ⦠H2) -H2 #H21 #H22 destruct
+/2 width=1 by conj/
+qed-.
+
+lemma ist_inv_zero_shift: âc. ðâ¦0,â*c⦠â ðâ¦0,câ¦.
+#c #H elim (ist_inv_shift ⦠H) -H //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
index bf3287912..474eb2778 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
@@ -12,7 +12,8 @@ table {
class "water"
[ { "generic rt-transition counter" * } {
[ { "" * } {
- [ "rtc ( â©?,?,?,?⪠) ( ðð ) ( ðð ) ( ðð )" "rtc_isrc ( ððâ¦?, ?⦠)" "rtc_shift ( â*? )" "rtc_max ( ? ⨠? )" "rtc_plus ( ? + ? )" * ]
+ [ "rtc_ist ( ðâ¦?,?⦠)" "rtc_ist_shift" "rtc_ist_plus" "rtc_ist_max" * ]
+ [ "rtc ( â©?,?,?,?⪠) ( ðð ) ( ðð ) ( ðð )" "rtc_isrc ( ððâ¦?,?⦠)" "rtc_shift ( â*? )" "rtc_max ( ? ⨠? )" "rtc_plus ( ? + ? )" * ]
}
]
}