made executable again

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

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 ec9cf1bb57e49d51f0dea0fa36f7945adf5cd64b..85afa3bab6601f187da907717b9fe223ead8a0b9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpxs.ma
@@ -13,52 +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 extended context-sensitive parallel rt-computation *******)
 
 lemma cpxs_fpbs:
-      â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T2 â\86\92 â\9dªG,L,T1â\9d« â\89¥ â\9dªG,L,T2â\9d«.
+      â\88\80G,L,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* T2 â\86\92 â\9d¨G,L,T1â\9d© â\89¥ â\9d¨G,L,T2â\9d©.
 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
-/3 width=5 by fpbq_cpx, fpbs_strap1/
+/3 width=5 by cpx_fpb, fpbs_strap1/
 qed.
 
 lemma fpbs_cpxs_trans:
-      â\88\80G1,G,L1,L,T1,T. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG,L,Tâ\9d« →
-      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\88* T2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG,L,T2â\9d«.
+      â\88\80G1,G,L1,L,T1,T. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G,L,Tâ\9d© →
+      â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â¬\88* T2 â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G,L,T2â\9d©.
 #G1 #G #L1 #L #T1 #T #H1 #T2 #H @(cpxs_ind … H) -T2
-/3 width=5 by fpbs_strap1, fpbq_cpx/
+/3 width=5 by fpbs_strap1, cpx_fpb/
 qed-.
 
 lemma cpxs_fpbs_trans:
-      â\88\80G1,G2,L1,L2,T,T2. â\9dªG1,L1,Tâ\9d« â\89¥ â\9dªG2,L2,T2â\9d« →
-      â\88\80T1. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* T â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+      â\88\80G1,G2,L1,L2,T,T2. â\9d¨G1,L1,Tâ\9d© â\89¥ â\9d¨G2,L2,T2â\9d© →
+      â\88\80T1. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88* T â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
 #G1 #G2 #L1 #L2 #T #T2 #H1 #T1 #H @(cpxs_ind_dx … H) -T1
-/3 width=5 by fpbs_strap2, fpbq_cpx/
+/3 width=5 by fpbs_strap2, cpx_fpb/
 qed-.
 
-lemma cpxs_teqx_fpbs_trans:
-      ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T → ∀T0. T ≛ T0 →
-      ∀G2,L2,T2. ❪G1,L1,T0❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
-/3 width=3 by cpxs_fpbs_trans, teqx_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_teqx_fpbs:
-      ∀G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈* T →
-      ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
-/4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ 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.
+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:
-      â\88\80G1,L1,T1,T. â\9dªG1,L1â\9d« ⊢ T1 ⬈* T →
-      â\88\80G2,L2,T2. â\9dªG1,L1,Tâ\9d« â¬\82+ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+      â\88\80G1,L1,T1,T. â\9d¨G1,L1â\9d© ⊢ T1 ⬈* T →
+      â\88\80G2,L2,T2. â\9d¨G1,L1,Tâ\9d© â¬\82+ â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
 /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.