milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
index 04b75e3ead82d4e864f3e4e73c42ed3710c61611..bcb4dea88470fe086eccdf69d1f98d2010f1c0d6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
@@ -15,23 +15,23 @@
 include "basic_2/rt_computation/cpxs_lpx.ma".
 include "basic_2/rt_computation/csx_cpxs.ma".
 
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
-(* Properties with unbound parallel rt-transition on all entries ************)
+(* Properties with extended parallel rt-transition on all entries ***********)
 
-lemma csx_lpx_conf (h) (G) (L1):
-      ∀T. ❪G,L1❫ ⊢ ⬈*𝐒[h] T →
-      ∀L2. ❪G,L1❫ ⊢ ⬈[h] L2 → ❪G,L2❫ ⊢ ⬈*𝐒[h] T.
-#h #G #L1 #T #H @(csx_ind_cpxs … H) -T
+lemma csx_lpx_conf (G) (L1):
+      ∀T. ❪G,L1❫ ⊢ ⬈*𝐒 T →
+      ∀L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T.
+#G #L1 #T #H @(csx_ind_cpxs … H) -T
 /4 width=3 by csx_intro, lpx_cpx_trans/
 qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma csx_abst (h) (G) (L):
-      ∀p,W. ❪G,L❫ ⊢ ⬈*𝐒[h] W →
-      ∀T. ❪G,L.ⓛW❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓛ[p]W.T.
-#h #G #L #p #W #HW
+lemma csx_abst (G) (L):
+      ∀p,W. ❪G,L❫ ⊢ ⬈*𝐒 W →
+      ∀T. ❪G,L.ⓛW❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ ⬈*𝐒 ⓛ[p]W.T.
+#G #L #p #W #HW
 @(csx_ind … HW) -W #W #_ #IHW #T #HT
 @(csx_ind … HT) -T #T #HT #IHT
 @csx_intro #X #H1 #H2
@@ -44,10 +44,10 @@ elim (tneqx_inv_pair  … H2) -H2
 ]
 qed.
 
-lemma csx_abbr (h) (G) (L):
-      ∀p,V. ❪G,L❫ ⊢ ⬈*𝐒[h] V →
-      ∀T. ❪G,L.ⓓV❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓓ[p]V.T.
-#h #G #L #p #V #HV
+lemma csx_abbr (G) (L):
+      ∀p,V. ❪G,L❫ ⊢ ⬈*𝐒 V →
+      ∀T. ❪G,L.ⓓV❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ ⬈*𝐒 ⓓ[p]V.T.
+#G #L #p #V #HV
 @(csx_ind … HV) -V #V #_ #IHV #T #HT
 @(csx_ind_cpxs … HT) -T #T #HT #IHT
 @csx_intro #X #H1 #H2
@@ -63,17 +63,17 @@ elim (cpx_inv_abbr1 … H1) -H1 *
 ]
 qed.
 
-lemma csx_bind (h) (G) (L):
-      ∀p,I,V. ❪G,L❫ ⊢ ⬈*𝐒[h] V →
-      ∀T. ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓑ[p,I]V.T.
-#h #G #L #p * #V #HV #T #HT
+lemma csx_bind (G) (L):
+      ∀p,I,V. ❪G,L❫ ⊢ ⬈*𝐒 V →
+      ∀T. ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ ⬈*𝐒 ⓑ[p,I]V.T.
+#G #L #p * #V #HV #T #HT
 /2 width=1 by csx_abbr, csx_abst/
 qed.
 
-fact csx_appl_theta_aux (h) (G) (L):
-     ∀p,U. ❪G,L❫ ⊢ ⬈*𝐒[h] U → ∀V1,V2. ⇧[1] V1 ≘ V2 →
-     ∀V,T. U = ⓓ[p]V.ⓐV2.T → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓐV1.ⓓ[p]V.T.
-#h #G #L #p #X #H
+fact csx_appl_theta_aux (G) (L):
+     ∀p,U. ❪G,L❫ ⊢ ⬈*𝐒 U → ∀V1,V2. ⇧[1] V1 ≘ V2 →
+     ∀V,T. U = ⓓ[p]V.ⓐV2.T → ❪G,L❫ ⊢ ⬈*𝐒 ⓐV1.ⓓ[p]V.T.
+#G #L #p #X #H
 @(csx_ind_cpxs … H) -X #X #HVT #IHVT #V1 #V2 #HV12 #V #T #H destruct
 lapply (csx_fwd_pair_sn … HVT) #HV
 lapply (csx_fwd_bind_dx … HVT) -HVT #HVT
@@ -105,7 +105,7 @@ elim (cpx_inv_appl1 … HL) -HL *
 ]
 qed-.
 
-lemma csx_appl_theta (h) (G) (L):
-      ∀p,V,V2,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓓ[p]V.ⓐV2.T →
-      ∀V1. ⇧[1] V1 ≘ V2 → ❪G,L❫ ⊢ ⬈*𝐒[h] ⓐV1.ⓓ[p]V.T.
+lemma csx_appl_theta (G) (L):
+      ∀p,V,V2,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓓ[p]V.ⓐV2.T →
+      ∀V1. ⇧[1] V1 ≘ V2 → ❪G,L❫ ⊢ ⬈*𝐒 ⓐV1.ⓓ[p]V.T.
 /2 width=5 by csx_appl_theta_aux/ qed.