update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
index c1e2b94c1cbca338c80ecd6d8c171b05faa39e26..2d33bdf492d5d1afe00a67e0f562dce3ea8d5e4d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
@@ -12,28 +12,54 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazybtpredstarproper_8.ma".
-include "basic_2/reduction/fpb.ma".
-include "basic_2/computation/fpbs.ma".
+include "ground_2/xoa/ex_2_3.ma".
+include "basic_2/notation/relations/predsubtystarproper_7.ma".
+include "basic_2/rt_transition/fpb.ma".
+include "basic_2/rt_computation/fpbs.ma".
 
-(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
+(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
-definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
-                 λh,o,G1,L1,T1,G2,L2,T2.
-                 â\88\83â\88\83G,L,T. â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G, L, Tâ¦\84 & â¦\83G, L, Tâ¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
+definition fpbg: ∀h. tri_relation genv lenv term ≝
+                 λh,G1,L1,T1,G2,L2,T2.
+                 â\88\83â\88\83G,L,T. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG,L,Tâ\9d« & â\9dªG,L,Tâ\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
 
-interpretation "'qrst' proper parallel computation (closure)"
-   'LazyBTPRedStarProper h o G1 L1 T1 G2 L2 T2 = (fpbg h o G1 L1 T1 G2 L2 T2).
+interpretation "proper parallel rst-computation (closure)"
+   'PRedSubTyStarProper h G1 L1 T1 G2 L2 T2 = (fpbg h G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fpb_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
-                â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G2, L2, T2â¦\84.
+lemma fpb_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ →
+                â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
 /2 width=5 by ex2_3_intro/ qed.
 
-lemma fpbg_fpbq_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 â\89½[h, o] â¦\83G2, L2, T2â¦\84 →
-                       â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
+lemma fpbg_fpbq_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
+                       â\9dªG1,L1,T1â\9d« >[h] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« â\89½[h] â\9dªG2,L2,T2â\9d« →
+                       â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
 /3 width=9 by fpbs_strap1, ex2_3_intro/
 qed-.
+
+lemma fpbg_fqu_trans (h): ∀G1,G,G2,L1,L,L2,T1,T,T2.
+                          ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G,L,T❫ ⬂ ❪G2,L2,T2❫ →
+                          ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
+qed-.
+
+(* Note: this is used in the closure proof *)
+lemma fpbg_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ →
+                       ∀G1,L1,T1. ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+#h #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
+qed-.
+
+(* Basic_2A1: uses: fpbg_fleq_trans *)
+lemma fpbg_feqx_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ >[h] ❪G,L,T❫ →
+                       ∀G2,L2,T2. ❪G,L,T❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+/3 width=5 by fpbg_fpbq_trans, fpbq_feqx/ qed-.
+
+(* Properties with t-bound rt-transition for terms **************************)
+
+lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
+                         ∀n1,T1,T. ❪G,L❫ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
+                         ∀n2,T2. ❪G,L❫ ⊢ T ➡[n2,h] T2 → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
+/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.