--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬆[ 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 }.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬆*[ 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 }.
--- /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_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 ≝
+ λT1,T2. ∃∃c. 𝐓⦃n,c⦄ & ⦃G,L⦄ ⊢ T1 ⬈[eq …,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):
+ ∀s. ⦃G,L⦄ ⊢ ⋆s ⬆[h,1] ⋆(⫯[h]s).
+/2 width=3 by cpg_ess, ex2_intro/ qed.
+
+lemma cpt_delta (h) (n) (G) (K):
+ ∀V1,V2. ⦃G,K⦄ ⊢ V1 ⬆[h,n] V2 →
+ ∀W2. ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓓV1⦄ ⊢ #0 ⬆[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):
+ ∀V1,V2. ⦃G,K⦄ ⊢ V1 ⬆[h,n] V2 →
+ ∀W2. ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓛV1⦄ ⊢ #0 ⬆[h,↑n] 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):
+ ∀T,i. ⦃G,K⦄ ⊢ #i ⬆[h,n] T → ∀U. ⇧*[1] T ≘ U →
+ ∀I. ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ⬆[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):
+ ∀V1,V2. ⦃G,L⦄ ⊢ V1 ⬆[h,0] V2 → ∀I,T1,T2. ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬆[h,n] T2 →
+ ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬆[h,n] ⓑ{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):
+ ∀V1,V2. ⦃G,L⦄ ⊢ V1 ⬆[h,0] V2 →
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ⦃G,L⦄ ⊢ ⓐV1.T1 ⬆[h,n] ⓐV2.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):
+ ∀U1,U2. ⦃G,L⦄ ⊢ U1 ⬆[h,n] U2 →
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ⦃G,L⦄ ⊢ ⓝU1.T1 ⬆[h,n] ⓝU2.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):
+ ∀U1,U2. ⦃G,L⦄ ⊢ U1 ⬆[h,n] U2 → ∀T. ⦃G,L⦄ ⊢ ⓝU1.T ⬆[h,↑n] 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):
+ ∀n. n ≤ 1 → ∀s. ⦃G,L⦄ ⊢ ⋆s ⬆[h,n] ⋆((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.
--- /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 "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):
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
+ ∃∃T0. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T0 & ⦃G,L⦄ ⊢ T0 ➡[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 (𝐔❴1❵)) #W0 #HVW0
+ lapply (cpm_lifts_bi … HV02 (Ⓣ) … (K.ⓓV1) … 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 (𝐔❴1❵)) #W0 #HVW0
+ lapply (cpm_lifts_bi … HV02 (Ⓣ) … (K.ⓛV1) … 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 (𝐔❴1❵)) #U0 #HTU0
+ lapply (cpm_lifts_bi … HT02 (Ⓣ) … (K.ⓘ{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 (Ⓣ) … (L.ⓓV) … 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):
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ⦃G,L⦄ ⊢ T1 ➡[n,h] T2.
\ No newline at end of file
--- /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 "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-.
]
class "cyan"
[ { "rt-transition" * } {
+ [ { "context-sensitive parallel t-transition" * } {
+ [ [ "for terms" ] "cpt" + "( ⦃?,?⦄ ⊢ ? ⬆[?,?] ? )" "cpt_drops" + "cpt_cpm" * ]
+ }
+ ]
[ { "context-sensitive parallel r-transition" * } {
[ [ "normal form for terms" ] "cnr ( ⦃?,?⦄ ⊢ ➡[?] 𝐍⦃?⦄ )" "cnr_simple" + "cnr_tdeq" + "cnr_drops" * ]
[ [ "for lenvs on all entries" ] "lpr" + "( ⦃?,?⦄ ⊢ ➡[?] ? )" "lpr_length" + "lpr_drops" + "lpr_fquq" + "lpr_aaa" + "lpr_lpx" + "lpr_lpr" * ]
--- /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 *)
+(* *)
+(**************************************************************************)
+
+(* GENERAL NOTATION USED BY THE FORMAL SYSTEM λδ ****************************)
+
+notation "hvbox( 𝐓⦃ term 46 n, break term 46 c ⦄ )"
+ non associative with precedence 45
+ for @{ 'IsType $n $c }.
--- /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_2/notation/relations/istype_2.ma".
+include "ground_2/steps/rtc.ma".
+
+(* T-TRANSITION COUNTER *****************************************************)
+
+definition ist: relation2 nat rtc ≝
+ λts,c. 〈0,0,0,ts〉 = c.
+
+interpretation "test for t-transition counter (rtc)"
+ 'IsType ts c = (ist ts c).
+
+(* Basic properties *********************************************************)
+
+lemma isr_00: 𝐓⦃0,𝟘𝟘⦄.
+// qed.
+
+lemma ist_01: 𝐓⦃1,𝟘𝟙⦄.
+// qed.
+
+(* Basic inversion properties ***********************************************)
+
+lemma ist_inv_00: ∀n. 𝐓⦃n,𝟘𝟘⦄ → 0 = n.
+#n #H destruct //
+qed-.
+
+lemma ist_inv_01: ∀n. 𝐓⦃n,𝟘𝟙⦄ → 1 = n.
+#n #H destruct //
+qed-.
+
+(* Main inversion properties ************************************************)
+
+theorem ist_inj: ∀n1,n2,c. 𝐓⦃n1,c⦄ → 𝐓⦃n2,c⦄ → n1 = n2.
+#n1 #n2 #c #H1 #H2 destruct //
+qed-.
+
+theorem ist_mono: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃n,c2⦄ → c1 = c2.
+#n #c1 #c2 #H1 #H2 destruct //
+qed-.
--- /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_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: ∀n1,n2,c1,c2. 𝐓⦃n1,c1⦄ → 𝐓⦃n2,c2⦄ → 𝐓⦃n1∨n2,c1∨c2⦄.
+#n1 #n2 #c1 #c2 #H1 #H2 destruct //
+qed.
+
+lemma ist_max_O1: ∀n,c1,c2. 𝐓⦃0,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄.
+/2 width=1 by ist_max/ qed.
+
+lemma ist_max_O2: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1∨c2⦄.
+#n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by ist_max/
+qed.
+
+lemma ist_max_idem1: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄.
+#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:
+ ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ →
+ ∃∃n1,n2. 𝐓⦃n1,c1⦄ & 𝐓⦃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: ∀c1,c2. 𝐓⦃0,c1 ∨ c2⦄ → ∧∧ 𝐓⦃0,c1⦄ & 𝐓⦃0,c2⦄.
+#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: ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1⦄.
+#n #c1 #c2 #H #H2
+elim (ist_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
+qed-.
--- /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_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: ∀n1,n2,c1,c2. 𝐓⦃n1,c1⦄ → 𝐓⦃n2,c2⦄ → 𝐓⦃n1+n2,c1+c2⦄.
+#n1 #n2 #c1 #c2 #H1 #H2 destruct //
+qed.
+
+lemma ist_plus_O1: ∀n,c1,c2. 𝐓⦃0,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1+c2⦄.
+/2 width=1 by ist_plus/ qed.
+
+lemma ist_plus_O2: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1+c2⦄.
+#n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by ist_plus/
+qed.
+
+lemma ist_succ: ∀n,c. 𝐓⦃n,c⦄ → 𝐓⦃↑n,c+𝟘𝟙⦄.
+/2 width=1 by ist_plus/ qed.
+
+(* Inversion properties with test for constrained rt-transition counter *****)
+
+lemma ist_inv_plus:
+ ∀n,c1,c2. 𝐓⦃n,c1 + c2⦄ →
+ ∃∃n1,n2. 𝐓⦃n1,c1⦄ & 𝐓⦃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: ∀n,c1,c2. 𝐓⦃n,c1 + c2⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1⦄.
+#n #c1 #c2 #H #H2
+elim (ist_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct //
+qed-.
+
+lemma ist_inv_plus_SO_dx:
+ ∀n,c1,c2. 𝐓⦃n,c1 + c2⦄ → 𝐓⦃1,c2⦄ →
+ ∃∃m. 𝐓⦃m,c1⦄ & n = ↑m.
+#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-.
--- /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_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: ∀c. 𝐓⦃0,c⦄ → 𝐓⦃0,↕*c⦄.
+#c #H destruct //
+qed.
+
+(* Inversion properties with test for t-transition counter ******************)
+
+lemma ist_inv_shift: ∀n,c. 𝐓⦃n,↕*c⦄ → ∧∧ 𝐓⦃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: ∀c. 𝐓⦃0,↕*c⦄ → 𝐓⦃0,c⦄.
+#c #H elim (ist_inv_shift … H) -H //
+qed-.
class "water"
[ { "generic rt-transition counter" * } {
[ { "" * } {
- [ "rtc ( 〈?,?,?,?〉 ) ( 𝟘𝟘 ) ( 𝟙𝟘 ) ( 𝟘𝟙 )" "rtc_isrc ( 𝐑𝐓⦃?, ?⦄ )" "rtc_shift ( ↕*? )" "rtc_max ( ? ∨ ? )" "rtc_plus ( ? + ? )" * ]
+ [ "rtc_ist ( 𝐓⦃?,?⦄ )" "rtc_ist_shift" "rtc_ist_plus" "rtc_ist_max" * ]
+ [ "rtc ( 〈?,?,?,?〉 ) ( 𝟘𝟘 ) ( 𝟙𝟘 ) ( 𝟘𝟙 )" "rtc_isrc ( 𝐑𝐓⦃?,?⦄ )" "rtc_shift ( ↕*? )" "rtc_max ( ? ∨ ? )" "rtc_plus ( ? + ? )" * ]
}
]
}
projects / helm.git / commitdiff