X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs_lpxs.ma;h=857f394d95f8a125d01c2aad6cda6bf7ad7de6aa;hp=f01561bc24af4902c9bc26026bf5196e66da383b;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

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 f01561bc2..857f394d9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
@@ -23,49 +23,49 @@ include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* Properties with unbound 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⦄.
+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
 /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⦄.
+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
 /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⦄.
+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
 /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: ∀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❫.
 /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: ∀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❫.
 /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: ∀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❫.
 /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
 
 (* Properties with unbound 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: ∀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❫.
 /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⦄.
+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
 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
 @(fpbs_fqup_trans … H34) -G2 -L4 -T2
@@ -75,18 +75,18 @@ 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: ∀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❫ .
 /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⦄.
+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
 [ /2 width=9 by ex4_5_intro/
 | #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0