X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffsb_fpbg.ma;h=afe69742678d7275ee52ac0f415c66387ced770b;hb=bc27cc1925469ddcd2bc3cd4036a6ea8067c5da1;hp=20c01020604940d60c04fb06237ff8bd01c8a160;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git

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 20c010206..afe697426 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
@@ -12,64 +12,76 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/fpbg_fpbs.ma".
-include "basic_2/rt_computation/fsb_feqx.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 ****************)
 
 (* Properties with parallel rst-computation for closures ********************)
 
-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
+lemma fsb_fpbs_trans:
+      ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
+#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=5 by fsb_feqx_trans/
-| -H1 * /2 width=5 by/
+[ -IH /2 width=9 by fsb_feqg_trans/
+| -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: ∀h,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.
+lemma fsb_intro_fpbg:
+      ∀G1,L1,T1.
+      (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) →
+      ≥𝐒 ❪G1,L1,T1❫.
+/4 width=1 by fsb_intro, fpbc_fpbg/ qed.
 
 (* Eliminators with proper parallel rst-computation for closures ************)
 
-lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
-                         (∀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. ≥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
+lemma fsb_ind_fpbg_fpbs (Q:relation3 …):
+      (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → 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: ∀h. ∀Q:relation3 genv lenv term.
-                    (∀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. ≥𝐒[h] ❪G1,L1,T1❫ →  Q G1 L1 T1.
-#h #Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
+lemma fsb_ind_fpbg (Q:relation3 …):
+      (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →  Q G1 L1 T1.
+#Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
 /3 width=1 by/
 qed-.
 
 (* Inversion lemmas with proper parallel rst-computation for closures *******)
 
-lemma fsb_fpbg_refl_false (h) (G) (L) (T):
-                          ≥𝐒[h] ❪G,L,T❫ → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.
-#h #G #L #T #H
+lemma fsb_fpbg_refl_false (G) (L) (T):
+      ≥𝐒 ❪G,L,T❫ → ❪G,L,T❫ > ❪G,L,T❫ → ⊥.
+#G #L #T #H
 @(fsb_ind_fpbg … H) -G -L -T #G1 #L1 #T1 #_ #IH #H
 /2 width=5 by/
 qed-.