update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 05bb29c012c541bf46b1a1cc9862ebd37a558616..756353fb35cc7b870355588c4ab8c80459d6ddac 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 +12,56 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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: ∀h,G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ≥[h] 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
+fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
+                      (∀G1,L1,T1,A. ❪G1,L1❫ ⊢ T1 ⁝ A →
+                                    (∀G2,L2,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → Q G2 L2 T2) →
+                                    Q G1 L1 T1
                       ) →
-                      â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\86\92 â\88\80A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
+                      â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\88\80A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92  Q G L T.
+#h #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.
-                   (â\88\80G1,L1,T1,A. â¦\83G1, L1â¦\84 ⊢ T1 ⁝ A →
-                                 (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
-                                 R G1 L1 T1
+lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
+                   (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+                                 (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d« â\86\92 Q G2 L2 T2) →
+                                 Q G1 L1 T1
                    ) →
-                   â\88\80G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
+                   â\88\80G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 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.
-                       (â\88\80G1,L1,T1,A. â¦\83G1, L1â¦\84 ⊢ T1 ⁝ A →
-                                     (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
-                                     R G1 L1 T1
+fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
+                       (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+                                     (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 Q G2 L2 T2) →
+                                     Q G1 L1 T1
                        ) →
-                       â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\86\92 â\88\80A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+                       â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\88\80A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92  Q G L T.
+#h #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.
-                    (â\88\80G1,L1,T1,A. â¦\83G1, L1â¦\84 ⊢ T1 ⁝ A →
-                                  (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
-                                  R G1 L1 T1
+lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
+                    (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+                                  (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 Q G2 L2 T2) →
+                                  Q G1 L1 T1
                     ) →
-                    â\88\80G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
+                    â\88\80G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 Q G L T.
 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.