milestone update in basic_2

[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 f9d110dd114aca54e9d5d8456e94480abf596319..4461f2f18b6a3ba6ba719522ca06b5afe8ffb763 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
@@ -13,7 +13,8 @@
 (**************************************************************************)
 
 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 ************************************)
 
@@ -22,39 +23,34 @@ include "basic_2/rt_computation/fpbs_fqup.ma".
 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 fpbq_cpx, fpbs_strap1/
+/3 width=5 by cpx_fpb, fpbs_strap1/
 qed.
 
 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, fpbq_cpx/
+/3 width=5 by fpbs_strap1, cpx_fpb/
 qed-.
 
 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, 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 →
+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=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
+/3 width=6 by cpxs_fpbs_trans, teqg_fpbs_trans/ qed-.
 
-lemma cpxs_teqx_fpbs:
+lemma cpxs_teqg_fpbs (S):
+      reflexive … S → symmetric … S →
       ∀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, teqg_feqg/ 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.
+      ∀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 **********)
 
@@ -62,3 +58,10 @@ 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.