milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
index 857f394d95f8a125d01c2aad6cda6bf7ad7de6aa..92fd0dd561db4a353e4de4dc056af4850f4e689b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
@@ -21,52 +21,60 @@ include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-(* Properties with unbound rt-computation on full local environments  *******)
+(* Properties with extended rt-computation on full local environments  ******)
 
-lemma lpxs_fpbs: ∀h,G,L1,L2,T. ❪G,L1❫ ⊢ ⬈*[h] L2 → ❪G,L1,T❫ ≥[h] ❪G,L2,T❫.
-#h #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
+lemma lpxs_fpbs:
+      ∀G,L1,L2,T. ❪G,L1❫ ⊢ ⬈* L2 → ❪G,L1,T❫ ≥ ❪G,L2,T❫.
+#G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
 /3 width=5 by fpbq_lpx, fpbs_strap1/
 qed.
 
-lemma fpbs_lpxs_trans: ∀h,G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L,T2❫ →
-                       ∀L2. ❪G2,L❫ ⊢ ⬈*[h] L2 → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-#h #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
+lemma fpbs_lpxs_trans:
+      ∀G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L,T2❫ →
+      ∀L2. ❪G2,L❫ ⊢ ⬈* L2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
 /3 width=5 by fpbs_strap1, fpbq_lpx/
 qed-.
 
-lemma lpxs_fpbs_trans: ∀h,G1,G2,L,L2,T1,T2. ❪G1,L,T1❫ ≥[h] ❪G2,L2,T2❫ →
-                       ∀L1. ❪G1,L1❫ ⊢ ⬈*[h] L → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-#h #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
+lemma lpxs_fpbs_trans:
+      ∀G1,G2,L,L2,T1,T2. ❪G1,L,T1❫ ≥ ❪G2,L2,T2❫ →
+      ∀L1. ❪G1,L1❫ ⊢ ⬈* L → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
 /3 width=5 by fpbs_strap2, fpbq_lpx/
 qed-.
 
 (* Basic_2A1: uses: lpxs_lleq_fpbs *)
-lemma lpxs_feqx_fpbs: ∀h,G1,L1,L,T1. ❪G1,L1❫ ⊢ ⬈*[h] L →
-                      ∀G2,L2,T2. ❪G1,L,T1❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+lemma lpxs_feqx_fpbs:
+      ∀G1,L1,L,T1. ❪G1,L1❫ ⊢ ⬈* L →
+      ∀G2,L2,T2. ❪G1,L,T1❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=3 by lpxs_fpbs_trans, feqx_fpbs/ qed.
 
-lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L,T2❫ →
-                      ∀L2. ❪G2,L❫ ⊢ ⬈[h] L2 → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+lemma fpbs_lpx_trans:
+      ∀G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L,T2❫ →
+      ∀L2. ❪G2,L❫ ⊢ ⬈ L2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ qed-.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma fqus_lpxs_fpbs: ∀h,G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ⬂* ❪G2,L,T2❫ →
-                      ∀L2. ❪G2,L❫ ⊢ ⬈*[h] L2 → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+lemma fqus_lpxs_fpbs:
+      ∀G1,G2,L1,L,T1,T2. ❪G1,L1,T1❫ ⬂* ❪G2,L,T2❫ →
+      ∀L2. ❪G2,L❫ ⊢ ⬈* L2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
 
-(* Properties with unbound context-sensitive parallel rt-computation ********)
+(* Properties with extended context-sensitive parallel rt-computation *******)
 
-lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
-                           ∀G2,L,T2. ❪G1,L1,T❫ ⬂* ❪G2,L,T2❫ →
-                           ∀L2.❪G2,L❫ ⊢ ⬈*[h] L2 → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+lemma cpxs_fqus_lpxs_fpbs:
+      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
+      ∀G2,L,T2. ❪G1,L1,T❫ ⬂* ❪G2,L,T2❫ →
+      ∀L2.❪G2,L❫ ⊢ ⬈* L2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
 
-lemma fpbs_cpxs_teqx_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ❪G1,L1,T1❫ ≥ [h] ❪G3,L3,T3❫ →
-                                     ∀T4. ❪G3,L3❫ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
-                                     ∀G2,L4,T2. ❪G3,L3,T5❫ ⬂+ ❪G2,L4,T2❫ →
-                                     ∀L2. ❪G2,L4❫ ⊢ ⬈[h] L2 → ❪G1,L1,T1❫ ≥ [h] ❪G2,L2,T2❫.
-#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
+lemma fpbs_cpxs_teqx_fqup_lpx_trans:
+      ∀G1,G3,L1,L3,T1,T3. ❪G1,L1,T1❫ ≥  ❪G3,L3,T3❫ →
+      ∀T4. ❪G3,L3❫ ⊢ T3 ⬈* T4 → ∀T5. T4 ≛ T5 →
+      ∀G2,L4,T2. ❪G3,L3,T5❫ ⬂+ ❪G2,L4,T2❫ →
+      ∀L2. ❪G2,L4❫ ⊢ ⬈ L2 → ❪G1,L1,T1❫ ≥  ❪G2,L2,T2❫.
+#G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
 @(fpbs_fqup_trans … H34) -G2 -L4 -T2
 /3 width=3 by fpbs_cpxs_trans, fpbs_teqx_trans/
@@ -75,19 +83,20 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: fpbs_intro_alt *)
-lemma fpbs_intro_star: ∀h,G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
-                       ∀G,L,T0. ❪G1,L1,T❫ ⬂* ❪G,L,T0❫ →
-                       ∀L0. ❪G,L❫ ⊢ ⬈*[h] L0 →
-                       ∀G2,L2,T2. ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ .
+lemma fpbs_intro_star:
+      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
+      ∀G,L,T0. ❪G1,L1,T❫ ⬂* ❪G,L,T0❫ →
+      ∀L0. ❪G,L❫ ⊢ ⬈* L0 →
+      ∀G2,L2,T2. ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ .
 /3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_feqx/ qed.
 
 (* Advanced inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: fpbs_inv_alt *)
-lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ →
-                     ∃∃G,L,L0,T,T0. ❪G1,L1❫ ⊢ T1 ⬈*[h] T & ❪G1,L1,T❫ ⬂* ❪G,L,T0❫
-                                  & ❪G,L❫ ⊢ ⬈*[h] L0 & ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
+lemma fpbs_inv_star:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ →
+      ∃∃G,L,L0,T,T0. ❪G1,L1❫ ⊢ T1 ⬈* T & ❪G1,L1,T❫ ⬂* ❪G,L,T0❫ & ❪G,L❫ ⊢ ⬈* L0 & ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
 [ /2 width=9 by ex4_5_intro/
 | #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0
   [ #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42