--- /dev/null
+(* Basic_1: was: pr3_pr1 *)
+lemma tprs_cprs: ∀G,L,T1,T2. ⦃G, ⋆⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
+/2 width=3 by lsubr_cprs_trans/ qed.
+
+(* Basic_1: was: nf2_pr3_unfold *)
+lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → T = U.
+#G #L #T #U #H @(cprs_ind_dx … H) -T //
+#T0 #T #H1T0 #_ #IHT #H2T0
+lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1 by/
+qed-.
+++ /dev/null
-
-lemma cprs_cpxs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈* T2 → ⦃G, L⦄ ⊢ T1 ⬈*[h] T2.
-#h #o #G #L #T1 #T2 #H @(cprs_ind … H) -T2 /3 width=3 by cpxs_strap1,
-cpr_cpx/
-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_computation/cpxs_aaa.ma".
+include "basic_2/rt_computation/cpms_cpxs.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Properties with atomic arity assignment on terms *************************)
+
+(* Basic_2A1: uses: scpds_aaa_conf *)
+(* Basic_2A1: includes: cprs_aaa_conf *)
+lemma cpms_aaa_conf (n) (h): ∀G,L. Conf3 … (aaa G L) (cpms h G L n).
+/3 width=5 by cpms_fwd_cpxs, cpxs_aaa_conf/ 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_cpx.ma".
+include "basic_2/rt_computation/cpxs.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Forward lemmas with unbound context-sensitive rt-computation for terms ***)
+
+(* Basic_2A1: includes: cprs_cpxs *)
+lemma cpms_fwd_cpxs (n) (h): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 → ⦃G, L⦄ ⊢ T1 ⬈*[h] T2.
+#n #h #G #L #T1 #T2 #H @(cpms_ind_dx … H) -T2
+/3 width=4 by cpxs_strap1, cpm_fwd_cpx/
+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_lsubr.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Properties with restricted refinement for local environments *************)
+
+(* Basic_2A1: uses: lsubr_cprs_trans *)
+lemma lsubr_cpms_trans (n) (h): ∀G. lsub_trans … (λL. cpms h G L n) lsubr.
+/3 width=5 by lsubr_cpm_trans, ltc_lsub_trans/
+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/reduction/lpx_aaa.ma".
-include "basic_2/computation/cpxs.ma".
-
-(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
-
-(* Properties about atomic arity assignment on terms ************************)
-
-lemma cpxs_aaa_conf: ∀h,o,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A →
- ∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
-#h #o #G #L #T1 #A #HT1 #T2 #HT12
-@(TC_Conf3 … HT1 ? HT12) -A -T1 -T2 /2 width=5 by cpx_aaa_conf/
-qed-.
-
-lemma cprs_aaa_conf: ∀G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ⬈* T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
-/3 width=5 by cpxs_aaa_conf, cprs_cpxs/ qed-.
+++ /dev/null
-lemma lsubr_cprs_trans: ∀G. lsub_trans … (cprs G) lsubr.
-/3 width=5 by lsubr_cpr_trans, CTC_lsub_trans/
-qed-.
-
-(* Basic_1: was: pr3_pr1 *)
-lemma tprs_cprs: ∀G,L,T1,T2. ⦃G, ⋆⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-/2 width=3 by lsubr_cprs_trans/ qed.
-
-(* Basic_1: was: nf2_pr3_unfold *)
-lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → T = U.
-#G #L #T #U #H @(cprs_ind_dx … H) -T //
-#T0 #T #H1T0 #_ #IHT #H2T0
-lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1 by/
-qed-.
fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_cpx.ma fpbs_fpb.ma fpbs_cpxs.ma fpbs_lpxs.ma fpbs_lfpxs.ma fpbs_csx.ma fpbs_fpbs.ma
fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_lfpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma
fsb.ma fsb_ffdeq.ma fsb_aaa.ma fsb_csx.ma fsb_fpbg.ma
-cpms.ma cpms_drops.ma
+cpms.ma cpms_drops.ma cpms_lsubr.ma cpms_aaa.ma cpms_cpxs.ma
cprs.ma cprs_drops.ma
+++ /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/unfold/lstas_aaa.ma".
-include "basic_2/computation/cpxs_aaa.ma".
-include "basic_2/computation/scpds.ma".
-
-(* STRATIFIED DECOMPOSED PARALLEL COMPUTATION ON TERMS **********************)
-
-(* Properties on atomic arity assignment for terms **************************)
-
-lemma scpds_aaa_conf: ∀h,o,G,L,d. Conf3 … (aaa G L) (scpds h o d G L).
-#h #o #G #L #d #A #T #HT #U * /3 width=6 by lstas_aaa_conf, cprs_aaa_conf/
-qed.
[ { "rt-computation" * } {
(*
[ { "decomposed rt-computation" * } {
- [ [ "" ] "scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )" "scpds_lift" + "scpds_aaa" + "scpds_scpds" * ]
+ "scpds_scpds"
}
]
*)
}
]
[ { "t-bound context-sensitive parallel rt-computation" * } {
- [ [ "for terms" ] "cpms" + "( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpms_drops" * ]
+ [ [ "for terms" ] "cpms" + "( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpms_drops" + "cpms_lsubr" + "cpms_aaa" + "cpms_cpxs" * ]
}
]
[ { "unbound context-sensitive parallel rst-computation" * } {
@(ltc_ind_dx … R … H1f … IH2 … H) -a -b2 -H1f #a #b2 #Hb12
>(H2f a) -H2f /3 width=4 by ltc_rc/
qed-.
+
+(* Properties with lsub *****************************************************)
+
+lemma ltc_lsub_trans: ∀A,f. associative … f →
+ ∀B,C,R,S. (∀n. lsub_trans B C (λL. R L n) S) →
+ ∀n. lsub_trans B C (λL. ltc A f … (R L) n) S.
+#A #f #Hf #B #C #R #S #HRS #n #L2 #T1 #T2 #H
+@(ltc_ind_dx … Hf ???? H) -n -T2
+/3 width=5 by ltc_dx, ltc_rc/
+qed-.
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