update in ground_2, static_2, basic_2, apps_2, alpha_1

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

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 07a9aad5eec9d8e0a714d1d7649c7bc85243e915..81583f39ea5fda52ad59d78f3c81afbe29705023 100644 (file)
--- 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_fdeq.ma".
+include "basic_2/rt_computation/fsb_feqx.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⦄ →
-                      â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â\89¥[h, o] ð\9d\90\92â¦\83G2, L2, T2â¦\84.
-#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❫ →
+                      â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« â\86\92 â\89¥[h] ð\9d\90\92â\9dªG2,L2,T2â\9d«.
+#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_fdeq_trans/
+[ -IH /2 width=5 by fsb_feqx_trans/
 | -H1 * /2 width=5 by/
 ]
 qed-.
 
 (* Properties with proper parallel rst-computation for closures *************)
 
-lemma fsb_intro_fpbg: ∀h,o,G1,L1,T1. (
-                         â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â\89¥[h, o] ð\9d\90\92â¦\83G2, L2, T2â¦\84
-                      ) → ≥[h, o] 𝐒⦃G1, L1, T1⦄.
+lemma fsb_intro_fpbg: ∀h,G1,L1,T1. (
+                         â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 â\89¥[h] ð\9d\90\92â\9dªG2,L2,T2â\9d«
+                      ) → ≥[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⦄ →
-                                     (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 → Q G2 L2 T2) →
+lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
+                         (∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+                                     (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
                                      Q G1 L1 T1
                          ) →
-                         ∀G1,L1,T1. ≥[h, o] 𝐒⦃G1, L1, T1⦄ → 
-                         â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84 → 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❫ →
+                         â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« → 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⦄ →
-                                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 → Q G2 L2 T2) →
+lemma fsb_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
+                    (∀G1,L1,T1. ≥[h] 𝐒❪G1,L1,T1❫ →
+                                (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → 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-.