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 c27ffaba51ed72e39b7c6c81e978131eaa6685e4..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
@@ -12,36 +12,40 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btsn_5.ma".
-include "basic_2/reduction/fpb.ma".
-include "basic_2/computation/csx.ma".
+include "basic_2/notation/relations/predsubtystrong_3.ma".
+include "basic_2/rt_transition/fpbc.ma".
 
-(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
+(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
-inductive fsb (h) (o): relation3 genv lenv term ≝
-| fsb_intro: ∀G1,L1,T1. (
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → fsb h o G2 L2 T2
-             ) → fsb h o G1 L1 T1
-.
+definition fsb: relation3 genv lenv term ≝
+           SN3 … fpb (feqg sfull).
 
 interpretation
-   "'qrst' strong normalization (closure)"
-   'BTSN h o G L T = (fsb h o G L T).
+  "strong normalization for parallel rst-transition (closure)"
+  'PRedSubTyStrong G L T = (fsb G L T).
 
-(* Basic eliminators ********************************************************)
+(* Basic properties *********************************************************)
 
-lemma fsb_ind_alt: ∀h,o. ∀R: relation3 …. (
-                      ∀G1,L1,T1. ⦥[h,o] ⦃G1, L1, T1⦄ → (
-                         ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2
-                      ) → R G1 L1 T1
-                   ) →
-                   ∀G,L,T. ⦥[h, o] ⦃G, L, T⦄ → R G L T.
-#h #o #R #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsb_intro/
-qed-.
+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 inversion lemmas ***************************************************)
+(* Basic eliminators ********************************************************)
 
-lemma fsb_inv_csx: ∀h,o,G,L,T. ⦥[h, o] ⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬊*[h, o] T.
-#h #o #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpb_cpx/
+(* Note: eliminator with shorter ground hypothesis *)
+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:
+              fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb
+              aaa_fsba
+*)