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 81583f39ea5fda52ad59d78f3c81afbe29705023..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
@@ -19,8 +19,8 @@ include "basic_2/rt_computation/fsb_feqx.ma".
 
 (* Properties with parallel rst-computation for closures ********************)
 
-lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
-                      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → ≥[h] 𝐒❪G2,L2,T2❫.
+lemma fsb_fpbs_trans: ∀h,G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
+                      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → ≥𝐒[h] ❪G2,L2,T2❫.
 #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
@@ -32,18 +32,18 @@ qed-.
 (* Properties with proper parallel rst-computation for closures *************)
 
 lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
-                         ∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → ≥[h] 𝐒❪G2,L2,T2❫
-                      ) → ≥[h] 𝐒❪G1,L1,T1❫.
+                         ∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → ≥𝐒[h] ❪G2,L2,T2❫
+                      ) → ≥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❫ →
+                         (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
                                      (∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
                                      Q G1 L1 T1
                          ) →
-                         ∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+                         ∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
                          ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → 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
@@ -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❫ →
+                    (∀G1,L1,T1. ≥𝐒[h] ❪G1,L1,T1❫ →
                                 (∀G2,L2,T2. ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫ → 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/