milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
index e40fbc1d3b1a33500c5fd4b9a57ea71c120b5941..b03c6a61533847c5df34d67db3c4f40faa11caff 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_aaa.ma
@@ -12,60 +12,61 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbs_aaa.ma".
-include "basic_2/computation/csx_aaa.ma".
-include "basic_2/computation/fsb_csx.ma".
+include "basic_2/rt_computation/csx_aaa.ma".
+include "basic_2/rt_computation/fpbs_aaa.ma".
+include "basic_2/rt_computation/fpbs_fpb.ma".
+include "basic_2/rt_computation/fsb_csx.ma".
 
-(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
+(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
-(* Main properties **********************************************************)
+(* Main properties with atomic arity assignment for terms *******************)
 
-(* Note: this is the "big tree" theorem ("RST" version) *)
-theorem aaa_fsb: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥[h, o] ⦃G, L, T⦄.
+theorem aaa_fsb:
+        ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ≥𝐒 ❪G,L,T❫.
 /3 width=2 by aaa_csx, csx_fsb/ qed.
 
-(* Note: this is the "big tree" theorem ("QRST" version) *)
-theorem aaa_fsba: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥⦥[h, o] ⦃G, L, T⦄.
-/3 width=2 by fsb_fsba, aaa_fsb/ qed.
+(* Advanced eliminators with atomic arity assignment for terms **************)
 
-(* Advanced eliminators on atomica arity assignment for terms ***************)
-
-fact aaa_ind_fpb_aux: ∀h,o. ∀R:relation3 genv lenv term.
-                      (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                    (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                    R G1 L1 T1
-                      ) →
-                      ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
+fact aaa_ind_fpb_aux (Q:relation3 …):
+     (∀G1,L1,T1,A.
+       ❪G1,L1❫ ⊢ T1 ⁝ A →
+       (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+       Q G1 L1 T1
+     ) →
+     ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
+#R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
-#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h o … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpb_fpbs/
 qed-.
 
-lemma aaa_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
-                   (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                 R G1 L1 T1
-                   ) →
-                   ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+lemma aaa_ind_fpb (Q:relation3 …):
+      (∀G1,L1,T1,A.
+        ❪G1,L1❫ ⊢ T1 ⁝ A →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
 /4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
 
-fact aaa_ind_fpbg_aux: ∀h,o. ∀R:relation3 genv lenv term.
-                       (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                     R G1 L1 T1
-                       ) →
-                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+fact aaa_ind_fpbg_aux (Q:relation3 …):
+     (∀G1,L1,T1,A.
+       ❪G1,L1❫ ⊢ T1 ⁝ A →
+       (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+       Q G1 L1 T1
+     ) →
+     ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A →  Q G L T.
+#Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
-#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h o … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpbg_fwd_fpbs/
 qed-.
 
-lemma aaa_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
-                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                  R G1 L1 T1
-                    ) →
-                    ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+lemma aaa_ind_fpbg (Q:relation3 …):
+      (∀G1,L1,T1,A.
+        ❪G1,L1❫ ⊢ T1 ⁝ A →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.