update in basic_2

[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 0ebebad3aaef9fddce10d502768f9d37a032215d..20c01020604940d60c04fb06237ff8bd01c8a160 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
@@ -13,18 +13,18 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/fpbg_fpbs.ma".
-include "basic_2/rt_computation/fsb_fdeq.ma".
+include "basic_2/rt_computation/fsb_feqx.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
 (* Properties with parallel rst-computation for closures ********************)
 
-lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →
-                      â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 â\86\92 â\89¥[h] ð\9d\90\92â¦\83G2,L2,T2â¦\84.
+lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+                      â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92[h] â\9dªG2,L2,T2â\9d«.
 #h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
 elim (fpbs_inv_fpbg … H12) -H12
-[ -IH /2 width=5 by fsb_fdeq_trans/
+[ -IH /2 width=5 by fsb_feqx_trans/
 | -H1 * /2 width=5 by/
 ]
 qed-.
@@ -32,19 +32,19 @@ qed-.
 (* Properties with proper parallel rst-computation for closures *************)
 
 lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
-                         â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84 â\86\92 â\89¥[h] ð\9d\90\92â¦\83G2,L2,T2â¦\84
-                      ) → ≥[h] 𝐒⦃G1,L1,T1⦄.
+                         â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92[h] â\9dªG2,L2,T2â\9d«
+                      ) → ≥𝐒[h] ❪G1,L1,T1❫.
 /4 width=1 by fsb_intro, fpb_fpbg/ qed.
 
 (* Eliminators with proper parallel rst-computation for closures ************)
 
 lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
-                         (∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →
-                                     (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+                         (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+                                     (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
                                      Q G1 L1 T1
                          ) →
-                         ∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ → 
-                         â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2.
+                         ∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+                         â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2.
 #h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
 @IH1 -IH1
@@ -56,11 +56,11 @@ lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
 qed-.
 
 lemma fsb_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
-                    (∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →
-                                (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+                    (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+                                (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
                                 Q G1 L1 T1
                     ) →
-                    ∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →  Q G1 L1 T1.
+                    ∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →  Q G1 L1 T1.
 #h #Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
 /3 width=1 by/
 qed-.
@@ -68,7 +68,7 @@ qed-.
 (* Inversion lemmas with proper parallel rst-computation for closures *******)
 
 lemma fsb_fpbg_refl_false (h) (G) (L) (T):
-                          ≥[h] 𝐒⦃G,L,T⦄ → ⦃G,L,T⦄ >[h] ⦃G,L,T⦄ → ⊥.
+                          ≥𝐒[h] ❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.
 #h #G #L #T #H
 @(fsb_ind_fpbg … H) -G -L -T #G1 #L1 #T1 #_ #IH #H
 /2 width=5 by/