update in ground and delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
index cdea1a3964a9f65d64d8f2549e3063a933713bb1..12c72dceb7e4c09444b0d56ccd49a63a5b594a88 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbg_fqup.ma".
+include "basic_2/rt_computation/fpbg_feqg.ma".
 include "basic_2/rt_computation/fsb_feqg.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
@@ -20,49 +21,58 @@ include "basic_2/rt_computation/fsb_feqg.ma".
 (* Properties with parallel rst-computation for closures ********************)
 
 lemma fsb_fpbs_trans:
-      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
-      â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92 â\9dªG2,L2,T2â\9d«.
-#G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+      â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d© â\86\92 â\89¥ð\9d\90\92 â\9d¨G2,L2,T2â\9d©.
+#G1 #L1 #T1 #H @(fsb_ind … H) -G1 -L1 -T1
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
 elim (fpbs_inv_fpbg … H12) -H12
 [ -IH /2 width=9 by fsb_feqg_trans/
-| -H1 * /2 width=5 by/
+| -H1 #H elim (fpbg_inv_fpbc_fpbs … H)
+  /2 width=5 by/
 ]
 qed-.
 
+(* Properties with parallel rst-transition for closures *********************)
+
+lemma fsb_fpb_trans:
+      ∀G1,L1,T1. ≥𝐒 ❨G1,L1,T1❩ →
+      ∀G2,L2,T2. ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩ → ≥𝐒 ❨G2,L2,T2❩.
+/3 width=5 by fsb_fpbs_trans, fpb_fpbs/ qed-.
+
 (* Properties with proper parallel rst-computation for closures *************)
 
 lemma fsb_intro_fpbg:
       ∀G1,L1,T1.
-      (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92 â\9dªG2,L2,T2â\9d«) →
-      â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d«.
-/4 width=1 by fsb_intro, fpb_fpbg/ qed.
+      (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© â\86\92 â\89¥ð\9d\90\92 â\9d¨G2,L2,T2â\9d©) →
+      â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d©.
+/4 width=1 by fsb_intro, fpbc_fpbg/ qed.
 
 (* Eliminators with proper parallel rst-computation for closures ************)
 
 lemma fsb_ind_fpbg_fpbs (Q:relation3 …):
-      (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
-        (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+      (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+        (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2) →
         Q G1 L1 T1
       ) →
-      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
-      â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d« → Q G2 L2 T2.
-#Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+      â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2.
+#Q #IH1 #G1 #L1 #T1 #H @(fsb_ind … H) -G1 -L1 -T1
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
 @IH1 -IH1
 [ -IH /2 width=5 by fsb_fpbs_trans/
 | -H1 #G0 #L0 #T0 #H10
-  elim (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2
+  lapply (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2 #H
+  elim (fpbg_inv_fpbc_fpbs … H) -H #G #L #T #H1 #H0
   /2 width=5 by/
 ]
 qed-.
 
 lemma fsb_ind_fpbg (Q:relation3 …):
-      (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
-        (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+      (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+        (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2) →
         Q G1 L1 T1
       ) →
-      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →  Q G1 L1 T1.
+      â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →  Q G1 L1 T1.
 #Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
 /3 width=1 by/
 qed-.
@@ -70,7 +80,7 @@ qed-.
 (* Inversion lemmas with proper parallel rst-computation for closures *******)
 
 lemma fsb_fpbg_refl_false (G) (L) (T):
-      â\89¥ð\9d\90\92 â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« > â\9dªG,L,Tâ\9d« → ⊥.
+      â\89¥ð\9d\90\92 â\9d¨G,L,Tâ\9d© â\86\92 â\9d¨G,L,Tâ\9d© > â\9d¨G,L,Tâ\9d© → ⊥.
 #G #L #T #H
 @(fsb_ind_fpbg … H) -G -L -T #G1 #L1 #T1 #_ #IH #H
 /2 width=5 by/