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=80ecd5486c6013f6c297173f41432fd1d93814ef;hp=07df0c6245afb41534f18f6407593caacc5c3dfc;hpb=f308429a0fde273605a2330efc63268b4ac36c99;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 07df0c624..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
@@ -12,98 +12,109 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/static/fdeq_fqus.ma".
-include "static_2/static/fdeq_fdeq.ma".
 include "basic_2/rt_computation/cpxs_fqus.ma".
-include "basic_2/rt_computation/cpxs_fdeq.ma".
-include "basic_2/rt_computation/lpxs_fdeq.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 unbound rt-computation on full local environments  *******)
+(* Properties with extended rt-computation on full local environments  ******)
 
-lemma lpxs_fpbs: ∀h,G,L1,L2,T. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → ⦃G,L1,T⦄ ≥[h] ⦃G,L2,T⦄.
-#h #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2
-/3 width=5 by fpbq_lpx, fpbs_strap1/
+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.
 
-lemma fpbs_lpxs_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L,T2⦄ →
-                       ∀L2. ⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2
-/3 width=5 by fpbs_strap1, fpbq_lpx/
+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: ∀h,G1,G2,L,L2,T1,T2. ⦃G1,L,T1⦄ ≥[h] ⦃G2,L2,T2⦄ →
-                       ∀L1. ⦃G1,L1⦄ ⊢ ⬈*[h] L → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1
-/3 width=5 by fpbs_strap2, fpbq_lpx/
+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_fdeq_fpbs: ∀h,G1,L1,L,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] L →
-                      ∀G2,L2,T2. ⦃G1,L,T1⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-/3 width=3 by lpxs_fpbs_trans, fdeq_fpbs/ qed.
-
-lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L,T2⦄ →
-                      ∀L2. ⦃G2,L⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-/3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ qed-.
+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: ∀h,G1,G2,L1,L,T1,T2. ⦃G1,L1,T1⦄ ⊐* ⦃G2,L,T2⦄ →
-                      ∀L2. ⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+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 unbound context-sensitive parallel rt-computation ********)
+(* Properties with extended context-sensitive parallel rt-computation *******)
 
-lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
-                           ∀G2,L,T2. ⦃G1,L1,T⦄ ⊐* ⦃G2,L,T2⦄ →
-                           ∀L2.⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+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_tdeq_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1,L1,T1⦄ ≥ [h] ⦃G3,L3,T3⦄ →
-                                     ∀T4. ⦃G3,L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
-                                     ∀G2,L4,T2. ⦃G3,L3,T5⦄ ⊐+ ⦃G2,L4,T2⦄ →
-                                     ∀L2. ⦃G2,L4⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥ [h] ⦃G2,L2,T2⦄.
-#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
+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=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/
+/3 width=6 by fpbs_cpxs_trans, fpbs_teqg_trans/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: fpbs_intro_alt *)
-lemma fpbs_intro_star: ∀h,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⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ .
-/3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_fdeq/ qed.
+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,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃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⦄ ≛ ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
-[ /2 width=9 by ex4_5_intro/
-| #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0
-  [ #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42
-    elim (fquq_cpxs_trans … HT03 … H10) -T0
-    /3 width=9 by fqus_strap2, ex4_5_intro/
-  | #T0 #HT10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42
-    /3 width=9 by cpxs_strap2, ex4_5_intro/
-  | #L0 #HL10 #_ * #G3 #L3 #L4 #T3 #T4 #HT13 #H34 #HL34 #H42
-    lapply (lpx_cpxs_trans … HT13 … HL10) -HT13 #HT13
-    elim (lpx_fqus_trans … H34 … HL10) -L0
-    /3 width=9 by lpxs_step_sn, cpxs_trans, ex4_5_intro/
-  | #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42
-    elim (fdeq_cpxs_trans … H10 … HT03) -T0 #T0 #HT10 #H03
-    elim (fdeq_fqus_trans … H03 … H34) -G0 -L0 -T3 #G0 #L0 #T3 #H03 #H34
-    elim (fdeq_lpxs_trans … H34 … HL34) -L3 #L3 #HL03 #H34
-    /3 width=13 by fdeq_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-.