X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs_cpxs.ma;h=4461f2f18b6a3ba6ba719522ca06b5afe8ffb763;hb=e23331eef5817eaa6c5e1c442d1d6bbb18650573;hp=4f23c0d0095759e30b7fe22eebf212f8bc76d6d8;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
index 4f23c0d00..4461f2f18 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
@@ -13,46 +13,55 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/cpxs.ma".
-include "basic_2/rt_computation/fpbs_fqup.ma".
+include "basic_2/rt_computation/fpbs_feqg.ma".
+include "basic_2/rt_computation/fpbs_fqus.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-(* Properties with unbound context-sensitive parallel rt-computation ********)
+(* Properties with extended context-sensitive parallel rt-computation *******)
 
-lemma cpxs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-#h #o #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
-/3 width=5 by fpbq_cpx, fpbs_strap1/
+lemma cpxs_fpbs:
+      ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
+#G #L #T1 #T2 #H @(cpxs_ind … H) -T2
+/3 width=5 by cpx_fpb, fpbs_strap1/
 qed.
 
-lemma fpbs_cpxs_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       ∀T2. ⦃G, L⦄ ⊢ T ⬈*[h] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-#h #o #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
-/3 width=5 by fpbs_strap1, fpbq_cpx/
+lemma fpbs_cpxs_trans:
+      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ∀T2. ❪G,L❫ ⊢ T ⬈* T2 → ❪G1,L1,T1❫ ≥ ❪G,L,T2❫.
+#G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
+/3 width=5 by fpbs_strap1, cpx_fpb/
 qed-.
 
-lemma cpxs_fpbs_trans: ∀h,o,G1,G2,L1,L2,T,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       ∀T1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
-/3 width=5 by fpbs_strap2, fpbq_cpx/
+lemma cpxs_fpbs_trans:
+      ∀G1,G2,L1,L2,T,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ →
+      ∀T1. ❪G1,L1❫ ⊢ T1 ⬈* T → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
+/3 width=5 by fpbs_strap2, cpx_fpb/
 qed-.
 
-lemma cpxs_tdeq_fpbs_trans: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                            ∀T0. T ≛[h, o] T0 →
-                            ∀G2,L2,T2. ⦃G1, L1, T0⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=3 by cpxs_fpbs_trans, tdeq_fpbs_trans/ qed-.
+lemma cpxs_teqg_fpbs_trans (S):
+      reflexive … S → symmetric … S →
+      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T → ∀T0. T ≛[S] T0 →
+      ∀G2,L2,T2. ❪G1,L1,T0❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=6 by cpxs_fpbs_trans, teqg_fpbs_trans/ qed-.
 
-lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
-                      ∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/4 width=3 by cpxs_fpbs_trans, fdeq_fpbs, tdeq_fdeq/ qed.
-
-(* Properties with star-iterated structural successor for closures **********)
-
-lemma cpxs_fqus_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
+lemma cpxs_teqg_fpbs (S):
+      reflexive … S → symmetric … S →
+      ∀G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈* T →
+      ∀T2. T ≛[S] T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
+/4 width=5 by cpxs_fpbs_trans, feqg_fpbs, teqg_feqg/ qed.
 
 (* Properties with plus-iterated structural successor for closures **********)
 
-lemma cpxs_fqup_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
-                      ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma cpxs_fqup_fpbs:
+      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
+      ∀G2,L2,T2. ❪G1,L1,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=5 by fpbs_fqup_trans, cpxs_fpbs/ qed.
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma cpxs_fqus_fpbs:
+      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
+      ∀G2,L2,T2. ❪G1,L1,T❫ ⬂* ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.