update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 f01561bc24af4902c9bc26026bf5196e66da383b..857f394d95f8a125d01c2aad6cda6bf7ad7de6aa 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
@@ -23,49 +23,49 @@ include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* Properties with unbound rt-computation on full local environments  *******)
 
-lemma lpxs_fpbs: â\88\80h,G,L1,L2,T. â¦\83G,L1â¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 â¦\83G,L1,Tâ¦\84 â\89¥[h] â¦\83G,L2,Tâ¦\84.
+lemma lpxs_fpbs: â\88\80h,G,L1,L2,T. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] L2 â\86\92 â\9dªG,L1,Tâ\9d« â\89¥[h] â\9dªG,L2,Tâ\9d«.
 #h #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
 /3 width=5 by fpbq_lpx, fpbs_strap1/
 qed.
 
-lemma fpbs_lpxs_trans: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L,T2â¦\84 →
-                       â\88\80L2. â¦\83G2,Lâ¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fpbs_lpxs_trans: â\88\80h,G1,G2,L1,L,T1,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L,T2â\9d« →
+                       â\88\80L2. â\9dªG2,Lâ\9d« â\8a¢ â¬\88*[h] L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 #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: â\88\80h,G1,G2,L,L2,T1,T2. â¦\83G1,L,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 →
-                       â\88\80L1. â¦\83G1,L1â¦\84 â\8a¢ â¬\88*[h] L â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma lpxs_fpbs_trans: â\88\80h,G1,G2,L,L2,T1,T2. â\9dªG1,L,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« →
+                       â\88\80L1. â\9dªG1,L1â\9d« â\8a¢ â¬\88*[h] L â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 #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: â\88\80h,G1,L1,L,T1. â¦\83G1,L1â¦\84 ⊢ ⬈*[h] L →
-                      â\88\80G2,L2,T2. â¦\83G1,L,T1â¦\84 â\89\9b â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma lpxs_feqx_fpbs: â\88\80h,G1,L1,L,T1. â\9dªG1,L1â\9d« ⊢ ⬈*[h] L →
+                      â\88\80G2,L2,T2. â\9dªG1,L,T1â\9d« â\89\9b â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=3 by lpxs_fpbs_trans, feqx_fpbs/ qed.
 
-lemma fpbs_lpx_trans: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L,T2â¦\84 →
-                      â\88\80L2. â¦\83G2,Lâ¦\84 â\8a¢ â¬\88[h] L2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fpbs_lpx_trans: â\88\80h,G1,G2,L1,L,T1,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L,T2â\9d« →
+                      â\88\80L2. â\9dªG2,Lâ\9d« â\8a¢ â¬\88[h] L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ qed-.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82* â¦\83G2,L,T2â¦\84 →
-                      â\88\80L2. â¦\83G2,Lâ¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82* â\9dªG2,L,T2â\9d« →
+                      â\88\80L2. â\9dªG2,Lâ\9d« â\8a¢ â¬\88*[h] L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
 
 (* Properties with unbound context-sensitive parallel rt-computation ********)
 
-lemma cpxs_fqus_lpxs_fpbs: â\88\80h,G1,L1,T1,T. â¦\83G1,L1â¦\84 ⊢ T1 ⬈*[h] T →
-                           â\88\80G2,L,T2. â¦\83G1,L1,Tâ¦\84 â¬\82* â¦\83G2,L,T2â¦\84 →
-                           â\88\80L2.â¦\83G2,Lâ¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma cpxs_fqus_lpxs_fpbs: â\88\80h,G1,L1,T1,T. â\9dªG1,L1â\9d« ⊢ T1 ⬈*[h] T →
+                           â\88\80G2,L,T2. â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG2,L,T2â\9d« →
+                           â\88\80L2.â\9dªG2,Lâ\9d« â\8a¢ â¬\88*[h] L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 /3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
 
-lemma fpbs_cpxs_teqx_fqup_lpx_trans: â\88\80h,G1,G3,L1,L3,T1,T3. â¦\83G1,L1,T1â¦\84 â\89¥ [h] â¦\83G3,L3,T3â¦\84 →
-                                     â\88\80T4. â¦\83G3,L3â¦\84 ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
-                                     â\88\80G2,L4,T2. â¦\83G3,L3,T5â¦\84 â¬\82+ â¦\83G2,L4,T2â¦\84 →
-                                     â\88\80L2. â¦\83G2,L4â¦\84 â\8a¢ â¬\88[h] L2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥ [h] â¦\83G2,L2,T2â¦\84.
+lemma fpbs_cpxs_teqx_fqup_lpx_trans: â\88\80h,G1,G3,L1,L3,T1,T3. â\9dªG1,L1,T1â\9d« â\89¥ [h] â\9dªG3,L3,T3â\9d« →
+                                     â\88\80T4. â\9dªG3,L3â\9d« ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
+                                     â\88\80G2,L4,T2. â\9dªG3,L3,T5â\9d« â¬\82+ â\9dªG2,L4,T2â\9d« →
+                                     â\88\80L2. â\9dªG2,L4â\9d« â\8a¢ â¬\88[h] L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ [h] â\9dªG2,L2,T2â\9d«.
 #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: â\88\80h,G1,L1,T1,T. â¦\83G1,L1â¦\84 ⊢ T1 ⬈*[h] T →
-                       â\88\80G,L,T0. â¦\83G1,L1,Tâ¦\84 â¬\82* â¦\83G,L,T0â¦\84 →
-                       â\88\80L0. â¦\83G,Lâ¦\84 ⊢ ⬈*[h] L0 →
-                       â\88\80G2,L2,T2. â¦\83G,L0,T0â¦\84 â\89\9b â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 .
+lemma fpbs_intro_star: â\88\80h,G1,L1,T1,T. â\9dªG1,L1â\9d« ⊢ T1 ⬈*[h] T →
+                       â\88\80G,L,T0. â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG,L,T0â\9d« →
+                       â\88\80L0. â\9dªG,Lâ\9d« ⊢ ⬈*[h] L0 →
+                       â\88\80G2,L2,T2. â\9dªG,L0,T0â\9d« â\89\9b 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 cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_feqx/ qed.
 
 (* Advanced inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: fpbs_inv_alt *)
-lemma fpbs_inv_star: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 →
-                     â\88\83â\88\83G,L,L0,T,T0. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] T & â¦\83G1,L1,Tâ¦\84 â¬\82* â¦\83G,L,T0â¦\84
-                                  & â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] L0 & â¦\83G,L0,T0â¦\84 â\89\9b â¦\83G2,L2,T2â¦\84.
+lemma fpbs_inv_star: â\88\80h,G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« →
+                     â\88\83â\88\83G,L,L0,T,T0. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88*[h] T & â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG,L,T0â\9d«
+                                  & â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] L0 & â\9dªG,L0,T0â\9d« â\89\9b â\9dªG2,L2,T2â\9d«.
 #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