update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fpbs_cpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
index 8500d2ddd8405f4a3ee566234ddd3bbe2225cd86..872882627045d743ec98602281c9a1af8e8fde72 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
@@ -12,43 +12,47 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/ffdeq_fqup.ma".
 include "basic_2/rt_computation/cpxs.ma".
 include "basic_2/rt_computation/fpbs_fqup.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-(* Properties with uncounted context-sensitive parallel rt-computation ******)
+(* Properties with unbound context-sensitive parallel rt-computation ********)
 
-lemma cpxs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-#h #o #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
+lemma cpxs_fpbs: ∀h,G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → ❪G,L,T1❫ ≥[h] ❪G,L,T2❫.
+#h #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=5 by fpbq_cpx, fpbs_strap1/
 qed.
 
-lemma fpbs_cpxs_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h] T2 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G, L, T2â¦\84.
-#h #o #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
+lemma fpbs_cpxs_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+                       â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\88*[h] T2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG,L,T2â\9d«.
+#h #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=5 by fpbs_strap1, fpbq_cpx/
 qed-.
 
-lemma cpxs_fpbs_trans: ∀h,o,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       â\88\80T1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h] T â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
+lemma cpxs_fpbs_trans: ∀h,G1,G2,L1,L2,T,T2. ❪G1,L1,T❫ ≥[h] ❪G2,L2,T2❫ →
+                       â\88\80T1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] T â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
 /3 width=5 by fpbs_strap2, fpbq_cpx/
 qed-.
 
-lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
-                      ∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/4 width=3 by cpxs_fpbs_trans, ffdeq_fpbs, tdeq_ffdeq/ qed.
+lemma cpxs_teqx_fpbs_trans: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
+                            ∀T0. T ≛ T0 →
+                            ∀G2,L2,T2. ❪G1,L1,T0❫ ≥[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+/3 width=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
+
+lemma cpxs_teqx_fpbs: ∀h,G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈*[h] T →
+                      ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥[h] ❪G,L,T2❫.
+/4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ qed.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma cpxs_fqus_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      â\88\80G2,L2,T2. â¦\83G1, L1, Tâ¦\84 â\8a\90* â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
+lemma cpxs_fqus_fpbs: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
+                      â\88\80G2,L2,T2. â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
 
 (* Properties with plus-iterated structural successor for closures **********)
 
-lemma cpxs_fqup_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      â\88\80G2,L2,T2. â¦\83G1, L1, Tâ¦\84 â\8a\90+ â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
+lemma cpxs_fqup_fpbs: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
+                      â\88\80G2,L2,T2. â\9dªG1,L1,Tâ\9d« â¬\82+ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.