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 8c4f35b6ca572dda243a2f0aee5ac33965e2edcc..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
@@ -15,28 +15,28 @@
 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⦄ →
-      â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] L2 â\86\92 â¦\83G,L2â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
-#h #G #L1 #T #H @(csx_ind_cpxs … H) -T
+lemma csx_lpx_conf (G) (L1):
+      ∀T. ❪G,L1❫ ⊢ ⬈*𝐒 T →
+      â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â¬\88 L2 â\86\92 â\9dªG,L2â\9d« â\8a¢ â¬\88*ð\9d\90\92 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⦄ →
-      â\88\80T. â¦\83G,L.â\93\9bWâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\9b{p}W.Tâ¦\84.
-#h #G #p #L #W #HW
+lemma csx_abst (G) (L):
+      ∀p,W. ❪G,L❫ ⊢ ⬈*𝐒 W →
+      â\88\80T. â\9dªG,L.â\93\9bWâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\9b[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
 elim (cpx_inv_abst1 … H1) -H1 #W0 #T0 #HLW0 #HLT0 #H destruct
-elim (tdneq_inv_pair  … H2) -H2
+elim (tneqx_inv_pair  … H2) -H2
 [ #H elim H -H //
 | -IHT #H lapply (csx_cpx_trans … HLT0) // -HT #HT0
   /4 width=5 by csx_lpx_conf, lpx_pair/
@@ -44,16 +44,16 @@ elim (tdneq_inv_pair  … H2) -H2
 ]
 qed.
 
-lemma csx_abbr (h) (G):
-      ∀p,L,V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-      â\88\80T. â¦\83G,L.â\93\93Vâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\93{p}V.Tâ¦\84.
-#h #G #p #L #V #HV
+lemma csx_abbr (G) (L):
+      ∀p,V. ❪G,L❫ ⊢ ⬈*𝐒 V →
+      â\88\80T. â\9dªG,L.â\93\93Vâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\93[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
 elim (cpx_inv_abbr1 … H1) -H1 *
 [ #V1 #T1 #HLV1 #HLT1 #H destruct
-  elim (tdneq_inv_pair … H2) -H2
+  elim (tneqx_inv_pair … H2) -H2
   [ #H elim H -H //
   | /4 width=5 by csx_cpx_trans, csx_lpx_conf, lpx_pair/
   | -IHV /4 width=3 by csx_cpx_trans, cpx_cpxs, cpx_pair_sn/
@@ -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⦄ →
-      â\88\80T. â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\91{p,I}V.Tâ¦\84.
-#h #G #p * #L #V #HV #T #HT
+lemma csx_bind (G) (L):
+      ∀p,I,V. ❪G,L❫ ⊢ ⬈*𝐒 V →
+      â\88\80T. â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\91[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
@@ -83,12 +83,12 @@ 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 (tdeq_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 (tdeq_inv_pair … H0) -H0 #_ #HV3 #H0
-      elim (tdeq_inv_pair … H0) -H0 #_ #HV24 #HT3
-      elim (tdneq_inv_pair … H) -H #H elim H -H -G -L
-      /3 width=6 by tdeq_inv_lifts_bi, tdeq_pair/
+      elim (teqx_inv_pair … H0) -H0 #_ #HV3 #H0
+      elim (teqx_inv_pair … H0) -H0 #_ #HV24 #HT3
+      elim (tneqx_inv_pair … H) -H #H elim H -H -G -L
+      /3 width=6 by teqx_inv_lifts_bi, teqx_pair/
     | -V1 @(IHVT … H0 … HV04) -V0 /4 width=1 by cpx_cpxs, cpx_flat, cpx_bind/
     ]
   | #T0 #HT0 #HLT0 #H0 destruct -H -IHVT
@@ -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⦄ →
-      â\88\80V1. â¬\86*[1] V1 â\89\98 V2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\90V1.â\93\93{p}V.Tâ¦\84.
+lemma csx_appl_theta (G) (L):
+      ∀p,V,V2,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓓ[p]V.ⓐV2.T →
+      â\88\80V1. â\87§[1] V1 â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\90V1.â\93\93[p]V.T.
 /2 width=5 by csx_appl_theta_aux/ qed.