update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex_fsle.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
index 7974bb900c8a1233f1139bd1cfd2a4e8f5a083c2..641fc459dad28879f9cbc9766457bb9447770a40 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_fsle.ma
@@ -20,21 +20,21 @@ include "static_2/static/rex_rex.ma".
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
 definition R_fsge_compatible: predicate (relation3 …) ≝ λRN.
-                              â\88\80L,T1,T2. RN L T1 T2 â\86\92 â¦\83L,T2â¦\84 â\8a\86 â¦\83L,T1â¦\84.
+                              â\88\80L,T1,T2. RN L T1 T2 â\86\92 â\9dªL,T2â\9d« â\8a\86 â\9dªL,T1â\9d«.
 
 definition rex_fsge_compatible: predicate (relation3 …) ≝ λRN.
-                                â\88\80L1,L2,T. L1 ⪤[RN,T] L2 â\86\92 â¦\83L2,Tâ¦\84 â\8a\86 â¦\83L1,Tâ¦\84.
+                                â\88\80L1,L2,T. L1 ⪤[RN,T] L2 â\86\92 â\9dªL2,Tâ\9d« â\8a\86 â\9dªL1,Tâ\9d«.
 
 definition rex_fsle_compatible: predicate (relation3 …) ≝ λRN.
-                                â\88\80L1,L2,T. L1 ⪤[RN,T] L2 â\86\92 â¦\83L1,Tâ¦\84 â\8a\86 â¦\83L2,Tâ¦\84.
+                                â\88\80L1,L2,T. L1 ⪤[RN,T] L2 â\86\92 â\9dªL1,Tâ\9d« â\8a\86 â\9dªL2,Tâ\9d«.
 
 (* Basic inversions with free variables inclusion for restricted closures ***)
 
 lemma frees_sex_conf (R):
       rex_fsge_compatible R →
-      â\88\80L1,T,f1. L1 â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f1 →
+      â\88\80L1,T,f1. L1 â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f1 →
       ∀L2. L1 ⪤[cext2 R,cfull,f1] L2 →
-      â\88\83â\88\83f2. L2 â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f2 & f2 ⊆ f1.
+      â\88\83â\88\83f2. L2 â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f2 & f2 ⊆ f1.
 #R #HR #L1 #T #f1 #Hf1 #L2 #H1L
 lapply (HR L1 L2 T ?) /2 width=3 by ex2_intro/ #H2L
 @(fsle_frees_trans_eq … H2L … Hf1) /3 width=4 by sex_fwd_length, sym_eq/
@@ -44,7 +44,7 @@ qed-.
 
 (* Note: we just need lveq_inv_refl: ∀L, n1, n2. L ≋ⓧ*[n1, n2] L → ∧∧ 0 = n1 & 0 = n2 *)
 lemma fsge_rex_trans (R):
-      â\88\80L1,T1,T2. â¦\83L1,T1â¦\84 â\8a\86 â¦\83L1,T2â¦\84 →
+      â\88\80L1,T1,T2. â\9dªL1,T1â\9d« â\8a\86 â\9dªL1,T2â\9d« →
       ∀L2. L1 ⪤[R,T2] L2 → L1 ⪤[R,T1] L2.
 #R #L1 #T1 #T2 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #Hn #Hf #L2 #HL12
 elim (lveq_inj_length … Hn ?) // #H1 #H2 destruct
@@ -65,11 +65,11 @@ lemma rex_pair_sn_split (R1) (R2):
       (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
       rex_fsge_compatible R1 →
       ∀L1,L2,V. L1 ⪤[R1,V] L2 → ∀I,T.
-      ∃∃L. L1 ⪤[R1,②{I}V.T] L & L ⪤[R2,V] L2.
+      ∃∃L. L1 ⪤[R1,②[I]V.T] L & L ⪤[R2,V] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #V * #f #Hf #HL12 * [ #p ] #I #T
-[ elim (frees_total L1 (ⓑ{p,I}V.T)) #g #Hg
+[ elim (frees_total L1 (ⓑ[p,I]V.T)) #g #Hg
   elim (frees_inv_bind … Hg) #y1 #y2 #H #_ #Hy
-| elim (frees_total L1 (ⓕ{I}V.T)) #g #Hg
+| elim (frees_total L1 (ⓕ[I]V.T)) #g #Hg
   elim (frees_inv_flat … Hg) #y1 #y2 #H #_ #Hy
 ]
 lapply(frees_mono … H … Hf) -H #H1
@@ -85,9 +85,9 @@ lemma rex_flat_dx_split (R1) (R2):
       (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
       rex_fsge_compatible R1 →
       ∀L1,L2,T. L1 ⪤[R1,T] L2 → ∀I,V.
-      ∃∃L. L1 ⪤[R1,ⓕ{I}V.T] L & L ⪤[R2,T] L2.
+      ∃∃L. L1 ⪤[R1,ⓕ[I]V.T] L & L ⪤[R2,T] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #I #V
-elim (frees_total L1 (ⓕ{I}V.T)) #g #Hg
+elim (frees_total L1 (ⓕ[I]V.T)) #g #Hg
 elim (frees_inv_flat … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 lapply (sor_eq_repl_back2 … Hy … H2) -y2 #Hy
@@ -101,10 +101,10 @@ qed-.
 lemma rex_bind_dx_split (R1) (R2):
       (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
       rex_fsge_compatible R1 →
-      ∀I,L1,L2,V1,T. L1.ⓑ{I}V1 ⪤[R1,T] L2 → ∀p.
-      ∃∃L,V. L1 ⪤[R1,ⓑ{p,I}V1.T] L & L.ⓑ{I}V ⪤[R2,T] L2 & R1 L1 V1 V.
+      ∀I,L1,L2,V1,T. L1.ⓑ[I]V1 ⪤[R1,T] L2 → ∀p.
+      ∃∃L,V. L1 ⪤[R1,ⓑ[p,I]V1.T] L & L.ⓑ[I]V ⪤[R2,T] L2 & R1 L1 V1 V.
 #R1 #R2 #HR1 #HR2 #HR #I #L1 #L2 #V1 #T * #f #Hf #HL12 #p
-elim (frees_total L1 (ⓑ{p,I}V1.T)) #g #Hg
+elim (frees_total L1 (ⓑ[p,I]V1.T)) #g #Hg
 elim (frees_inv_bind … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 lapply (tl_eq_repl … H2) -H2 #H2
@@ -123,9 +123,9 @@ lemma rex_bind_dx_split_void (R1) (R2):
       (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
       rex_fsge_compatible R1 →
       ∀L1,L2,T. L1.ⓧ ⪤[R1,T] L2 → ∀p,I,V.
-      ∃∃L. L1 ⪤[R1,ⓑ{p,I}V.T] L & L.ⓧ ⪤[R2,T] L2.
+      ∃∃L. L1 ⪤[R1,ⓑ[p,I]V.T] L & L.ⓧ ⪤[R2,T] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #p #I #V
-elim (frees_total L1 (ⓑ{p,I}V.T)) #g #Hg
+elim (frees_total L1 (ⓑ[p,I]V.T)) #g #Hg
 elim (frees_inv_bind_void … Hg) #y1 #y2 #_ #H #Hy
 lapply(frees_mono … H … Hf) -H #H2
 lapply (tl_eq_repl … H2) -H2 #H2