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=806180ead0f58ca5a7ea3a381f9d83c00287a098;hb=4173283e148199871d787c53c0301891deb90713;hp=b2093e068389d718efe3bc206056cd1459ea4453;hpb=5c186c72f508da0849058afeecc6877cd9ed6303;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 b2093e068..806180ead 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
@@ -13,39 +13,39 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/fpbg_fpbs.ma".
-include "basic_2/rt_computation/fsb_ffdeq.ma".
+include "basic_2/rt_computation/fsb_fdeq.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
 (* Properties with parallel rst-computation for closures ********************)
 
-lemma fsb_fpbs_trans: ∀h,o,G1,L1,T1. ≥[h, o] 𝐒⦃G1, L1, T1⦄ →
-                      ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄.
-#h #o #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+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⦄.
+#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_ffdeq_trans/
+[ -IH /2 width=5 by fsb_fdeq_trans/
 | -H1 * /2 width=5 by/
 ]
 qed-.
 
 (* Properties with proper parallel rst-computation for closures *************)
 
-lemma fsb_intro_fpbg: ∀h,o,G1,L1,T1. (
-                         ∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄
-                      ) → ≥[h, o] 𝐒⦃G1, L1, T1⦄.
+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⦄.
 /4 width=1 by fsb_intro, fpb_fpbg/ qed.
 
 (* Eliminators with proper parallel rst-computation for closures ************)
 
-lemma fsb_ind_fpbg_fpbs: ∀h,o. ∀Q:relation3 genv lenv term.
-                         (∀G1,L1,T1. ≥[h, o] 𝐒⦃G1, L1, T1⦄ →
-                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
+                         (∀G1,L1,T1. ≥[h] 𝐒⦃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, o] 𝐒⦃G1, L1, T1⦄ → 
-                         ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
-#h #o #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+                         ∀G1,L1,T1. ≥[h] 𝐒⦃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
 @IH1 -IH1
 [ -IH /2 width=5 by fsb_fpbs_trans/
@@ -55,12 +55,21 @@ lemma fsb_ind_fpbg_fpbs: ∀h,o. ∀Q:relation3 genv lenv term.
 ]
 qed-.
 
-lemma fsb_ind_fpbg: ∀h,o. ∀Q:relation3 genv lenv term.
-                    (∀G1,L1,T1. ≥[h, o] 𝐒⦃G1, L1, T1⦄ →
-                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+lemma fsb_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
+                    (∀G1,L1,T1. ≥[h] 𝐒⦃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, o] 𝐒⦃G1, L1, T1⦄ →  Q G1 L1 T1.
-#h #o #Q #IH #G1 #L1 #T1 #H @(fsb_ind_fpbg_fpbs … H) -H
+                    ∀G1,L1,T1. ≥[h] 𝐒⦃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-.
+
+(* 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⦄ → ⊥.
+#h #G #L #T #H
+@(fsb_ind_fpbg … H) -G -L -T #G1 #L1 #T1 #_ #IH #H
+/2 width=5 by/
+qed-.