milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
index 2118c2c16b9ce59b7b296fccb0775d30525b9ee1..a1ac691824c89bc946a8a9fc477a1f216c2cc6f1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
@@ -12,57 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/lpxs_lleq.ma".
-include "basic_2/computation/fpbs_lift.ma".
-include "basic_2/computation/fpbg_fleq.ma".
+include "basic_2/rt_computation/fpbs_fpbs.ma".
+include "basic_2/rt_computation/fpbg.ma".
 
-(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
+(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
-(* Properties on "qrst" parallel reduction on closures **********************)
+(* Advanced forward lemmas **************************************************)
 
-lemma fpb_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ ≻[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≛[h, o] ⦃G2, L2, T2⦄ →
-                      ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
-
-lemma fpbq_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       ⦃G1, L1, T1⦄ ≽[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≛[h, o] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fpbq_ind_alt … H1) -H1
-/2 width=5 by fleq_fpbg_trans, fpb_fpbg_trans/
+lemma fpbg_fwd_fpbs (G1) (G2) (L1) (L2) (T1) (T2):
+      ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 #H
+elim (fpbg_inv_gen … H) -H
+/4 width=9 by fpbs_trans, fpbs_strap2, fpbc_fwd_fpb/
 qed-.
 
-(* Properties on "qrst" parallel compuutation on closures *******************)
+(* Advanced properties ******************************************************)
 
-lemma fpbs_fpbg_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ >≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
+lemma fpbs_fpbg_trans (G) (L) (T):
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
+elim (fpbg_inv_gen … H2) -H2
+/3 width=13 by fpbg_intro, fpbs_trans/
 qed-.
 
 (* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
+lemma fpbg_fpbs_trans (G) (L) (T):
+      ∀G1,L1,T1. ❪G1,L1,T1❫ > ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
+elim (fpbg_inv_gen … H1) -H1
+/3 width=13 by fpbg_intro, fpbs_trans/
 qed-.
-
-(* Note: this is used in the closure proof *)
-lemma fqup_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqup_inv_step_sn … H) -H
-/3 width=5 by fqus_fpbs, fpb_fqu, ex2_3_intro/
-qed.
-
-lemma cpxs_fpbg: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 →
-                 (T1 = T2 → ⊥) → ⦃G, L, T1⦄ >≛[h, o] ⦃G, L, T2⦄.
-#h #o #G #L #T1 #T2 #H #H0 elim (cpxs_neq_inv_step_sn … H … H0) -H -H0
-/4 width=5 by cpxs_fpbs, fpb_cpx, ex2_3_intro/
-qed.
-
-lemma lstas_fpbg: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → (T1 = T2 → ⊥) →
-                  ∀d1. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → ⦃G, L, T1⦄ >≛[h, o] ⦃G, L, T2⦄.
-/3 width=5 by lstas_cpxs, cpxs_fpbg/ qed.
-
-lemma lpxs_fpbg: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 →
-                 (L1 ≡[T, 0] L2 → ⊥) → ⦃G, L1, T⦄ >≛[h, o] ⦃G, L2, T⦄.
-#h #o #G #L1 #L2 #T #H #H0 elim (lpxs_nlleq_inv_step_sn … H … H0) -H -H0
-/4 width=5 by fpb_lpx, lpxs_lleq_fpbs, ex2_3_intro/
-qed.