X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs_lpxs.ma;h=6a5363a99852e3774d85ce9052bf9b1e8bf631ab;hb=7c9d99dfb049d726491b71f07ba6a9b088b30166;hp=8a0a1840563bf358ccd6aa58c82fb22f3777c234;hpb=97c627e9d169b5df0308d440a449a6853108f372;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
index 8a0a18405..6a5363a99 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
@@ -12,29 +12,109 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/ffdeq_lfeq.ma".
-include "basic_2/rt_computation/lfpxs_lpxs.ma".
-include "basic_2/rt_computation/fpbs_lfpxs.ma".
+include "basic_2/rt_computation/cpxs_fqus.ma".
+include "basic_2/rt_computation/cpxs_reqg.ma".
+include "basic_2/rt_computation/lpxs_feqg.ma".
+include "basic_2/rt_computation/fpbs_lpx.ma".
+include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-(* Properties with uncounted parallel rt-computation on local environments **)
+(* Properties with extended rt-computation on full local environments  ******)
 
-(* Basic_2A1: uses: fpbs_intro_alt *) 
-lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                       ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ →
-                       ∀L0. ⦃G, L⦄ ⊢ ⬈*[h] L0 →
-                       ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ .
-/3 width=9 by fpbs_intro_fstar, lfpxs_lpxs/ qed.
+lemma lpxs_fpbs:
+      ∀G,L1,L2,T. ❨G,L1❩ ⊢ ⬈* L2 → ❨G,L1,T❩ ≥ ❨G,L2,T❩.
+#G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
+/3 width=5 by lpx_fpb, fpbs_strap1/
+qed.
 
-(* Eliminators with uncounted parallel rt-computation on local environments *)
+lemma fpbs_lpxs_trans:
+      ∀G1,G2,L1,L,T1,T2. ❨G1,L1,T1❩ ≥ ❨G2,L,T2❩ →
+      ∀L2. ❨G2,L❩ ⊢ ⬈* L2 → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
+/3 width=5 by fpbs_strap1, lpx_fpb/
+qed-.
+
+lemma lpxs_fpbs_trans:
+      ∀G1,G2,L,L2,T1,T2. ❨G1,L,T1❩ ≥ ❨G2,L2,T2❩ →
+      ∀L1. ❨G1,L1❩ ⊢ ⬈* L → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
+/3 width=5 by fpbs_strap2, lpx_fpb/
+qed-.
+
+(* Basic_2A1: uses: lpxs_lleq_fpbs *)
+lemma lpxs_feqg_fpbs (S) (L):
+      reflexive … S → symmetric … S →
+      ∀G1,L1,T1. ❨G1,L1❩ ⊢ ⬈* L →
+      ∀G2,L2,T2. ❨G1,L,T1❩ ≛[S] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+/3 width=4 by lpxs_fpbs_trans, feqg_fpbs/ qed.
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma fqus_lpxs_fpbs:
+      ∀G1,G2,L1,L,T1,T2. ❨G1,L1,T1❩ ⬂* ❨G2,L,T2❩ →
+      ∀L2. ❨G2,L❩ ⊢ ⬈* L2 → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+/3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
+
+(* Properties with extended context-sensitive parallel rt-computation *******)
+
+lemma cpxs_fqus_lpxs_fpbs:
+      ∀G1,L1,T1,T. ❨G1,L1❩ ⊢ T1 ⬈* T →
+      ∀G2,L,T2. ❨G1,L1,T❩ ⬂* ❨G2,L,T2❩ →
+      ∀L2.❨G2,L❩ ⊢ ⬈* L2 → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+/3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
+
+lemma fpbs_cpxs_teqg_fqup_lpx_trans (S):
+      reflexive … S → symmetric … S →
+      ∀G1,G3,L1,L3,T1,T3. ❨G1,L1,T1❩ ≥  ❨G3,L3,T3❩ →
+      ∀T4. ❨G3,L3❩ ⊢ T3 ⬈* T4 → ∀T5. T4 ≛[S] T5 →
+      ∀G2,L4,T2. ❨G3,L3,T5❩ ⬂+ ❨G2,L4,T2❩ →
+      ∀L2. ❨G2,L4❩ ⊢ ⬈ L2 → ❨G1,L1,T1❩ ≥  ❨G2,L2,T2❩.
+#S #H1S #H2S #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
+@(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
+@(fpbs_fqup_trans … H34) -G2 -L4 -T2
+/3 width=6 by fpbs_cpxs_trans, fpbs_teqg_trans/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: fpbs_intro_alt *)
+lemma fpbs_intro_star (S) (G) (T) (T0) (L) (L0):
+      reflexive … S → symmetric … S →
+      ∀G1,L1,T1. ❨G1,L1❩ ⊢ T1 ⬈* T →
+      ❨G1,L1,T❩ ⬂* ❨G,L,T0❩ → ❨G,L❩ ⊢ ⬈* L0 →
+      ∀G2,L2,T2. ❨G,L0,T0❩ ≛[S] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+/3 width=8 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, feqg_fpb/ qed.
+
+(* Advanced inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: fpbs_inv_alt *)
-lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                     ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄
-                                  & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H
-elim (fpbs_inv_fstar … H) -H #G #L #L0 #T #T0 #HT1 #H10 #HL0 #H02
-elim (lfpxs_inv_lpxs_lfeq … HL0) -HL0 #L3 #HL3 #HL30
-/3 width=11 by lfeq_lfdeq_trans, ex4_5_intro/
+lemma fpbs_inv_star (S):
+      reflexive … S → symmetric … S → Transitive  … S → 
+      ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩ →
+      ∃∃G,L,L0,T,T0. ❨G1,L1❩ ⊢ T1 ⬈* T & ❨G1,L1,T❩ ⬂* ❨G,L,T0❩ & ❨G,L❩ ⊢ ⬈* L0 & ❨G,L0,T0❩ ≛[S] ❨G2,L2,T2❩.
+#S #H1S #H2S #H3S #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
+[ /3 width=9 by feqg_refl, ex4_5_intro/
+| #G1 #G0 #L1 #L0 #T1 #T0 *
+  #L3 #T3 #H13 #HT30 #HL30 #_ *
+  #G4 #L4 #L5 #T4 #T5 #HT04 #H45 #HL45 #H52
+  lapply (rpx_cpx_conf_sn … HT30 … HL30) -HL30 #HL30
+  elim (fquq_cpx_trans … H13 … HT30) -T3 #T3 #HT13 #H30
+  elim (rpx_fwd_lpx_reqg S … HL30) -HL30 // #L #HL3 #HL0
+  lapply (reqg_cpxs_trans … HT04 … HL0) -HT04 // #HT04
+  lapply (cpxs_reqg_conf_sn … HT04 … HL0) -HL0 #HL0
+  lapply (lpx_cpxs_trans … HT04 … HL3) -HT04 #HT04
+  elim (fquq_cpxs_trans … HT04 … H30) -T0 #T0 #HT30 #H04
+  lapply (cpxs_strap2 … HT13 … HT30) -T3 #HT10
+  elim (reqg_fqus_trans … H45 … HL0) -L0 // #L0 #T3 #H43 #HT35 #HL04
+  lapply (feqg_intro_dx … G4 … HL04 … HT35) -HL04 -HT35 // #H35
+  elim (lpx_fqus_trans … H43 … HL3) -L #L #T #HT4 #H3 #HL0
+  elim (fquq_cpxs_trans … HT4 … H04) -T4 #T4 #HT04 #H4
+  lapply (cpxs_trans … HT10 … HT04) -T0 #HT14
+  lapply (fqus_strap2 … H4 … H3) -G0 -L3 -T #H43
+  elim (feqg_lpxs_trans … H35 … HL45) -L4 // #L4 #HL04 #H35
+  lapply (lpxs_step_sn … HL0 … HL04) -L0 #HL4
+  lapply (feqg_trans … H35 … H52) -L5 -T5 // #H32
+  /2 width=9 by ex4_5_intro/
+]
 qed-.