X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_lpx.ma;h=bcb4dea88470fe086eccdf69d1f98d2010f1c0d6;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=79d69cf4c7b0f74994ffd1c96a5f91849dacd538;hpb=adb9ba187619cea977d1d22971eba27eb437cd6a;p=helm.git

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 79d69cf4c..bcb4dea88 100644
--- 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⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →
-      ∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → ⦃G,L2⦄ ⊢ ⬈*[h] 𝐒⦃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):
-      ∀p,L,W. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃W⦄ →
-      ∀T. ⦃G,L.ⓛW⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓛ{p}W.T⦄.
-#h #G #p #L #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):
-      ∀p,L,V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-      ∀T. ⦃G,L.ⓓV⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.T⦄.
-#h #G #p #L #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):
-      ∀p,I,L,V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-      ∀T. ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄.
-#h #G #p * #L #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):
-     ∀p,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ → ∀V1,V2. ⇧*[1] V1 ≘ V2 →
-     ∀V,T. U = ⓓ{p}V.ⓐV2.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
-#h #G #p #L #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
@@ -83,7 +83,7 @@ elim (cpx_inv_appl1 … HL) -HL *
   elim (cpx_inv_abbr1 … HL) -HL *
   [ #V3 #T3 #HV3 #HLT3 #H0 destruct
     elim (cpx_lifts_sn … HLV10 (Ⓣ) … (L.ⓓV) … HV12) -HLV10 /3 width=1 by drops_refl, drops_drop/ #V4 #HV04 #HV24
-    elim (teqx_dec (ⓓ{p}V.ⓐV2.T) (ⓓ{p}V3.ⓐV4.T3)) #H0
+    elim (teqx_dec (ⓓ[p]V.ⓐV2.T) (ⓓ[p]V3.ⓐV4.T3)) #H0
     [ -IHVT -HV3 -HV24 -HLT3
       elim (teqx_inv_pair … H0) -H0 #_ #HV3 #H0
       elim (teqx_inv_pair … H0) -H0 #_ #HV24 #HT3
@@ -105,7 +105,7 @@ elim (cpx_inv_appl1 … HL) -HL *
 ]
 qed-.
 
-lemma csx_appl_theta (h) (G):
-      ∀p,L,V,V2,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.ⓐV2.T⦄ →
-      ∀V1. ⇧*[1] V1 ≘ V2 → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐ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.