update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
index e5a0108c3383bcfb0da418c525187851c034af1b..3f4ccd360a0e953f202d6b6fec77b0f48757b690 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
@@ -12,33 +12,37 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsubtystrong_4.ma".
-include "basic_2/rt_transition/fpb.ma".
+include "basic_2/notation/relations/predsubtystrong_3.ma".
+include "basic_2/rt_transition/fpbc.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
-inductive fsb (h): relation3 genv lenv term ≝
-| fsb_intro: ∀G1,L1,T1. (
-                ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → fsb h G2 L2 T2
-             ) → fsb h G1 L1 T1
-.
+definition fsb: relation3 genv lenv term ≝
+           SN3 … fpb (feqg sfull).
 
 interpretation
-   "strong normalization for parallel rst-transition (closure)"
-   'PRedSubTyStrong h G L T = (fsb h G L T).
+  "strong normalization for parallel rst-transition (closure)"
+  'PRedSubTyStrong G L T = (fsb G L T).
+
+(* Basic properties *********************************************************)
+
+lemma fsb_intro (G1) (L1) (T1):
+      (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) → ≥𝐒 ❪G1,L1,T1❫.
+/5 width=1 by fpbc_intro, SN3_intro/ qed.
 
 (* Basic eliminators ********************************************************)
 
 (* Note: eliminator with shorter ground hypothesis *)
-(* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
-lemma fsb_ind_alt: ∀h. ∀Q: relation3 …. (
-                      ∀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
-                   ) →
-                   ∀G,L,T. ≥[h] 𝐒⦃G,L,T⦄ →  Q G L T.
-#h #Q #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsb_intro/
+lemma fsb_ind (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
+      ) →
+      ∀G,L,T. ≥𝐒 ❪G,L,T❫ → Q G L T.
+#Q #IH #G #L #T #H elim H -G -L -T
+#G1 #L1 #T1 #H1 #IH1
+@IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H
+elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12 /3 width=1 by/
 qed-.
 
 (* Basic_2A1: removed theorems 6: