milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
index d88452162cbde3924f62de271bbe230a926da58f..c5d14bbe2273e6a3e619775570991d57e7a9ec79 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx_vector.ma
@@ -18,15 +18,15 @@ include "basic_2/rt_computation/csx_lsubr.ma".
 include "basic_2/rt_computation/csx_lpx.ma".
 include "basic_2/rt_computation/csx_vector.ma".
 
-(* STRONGLY NORMALIZING TERM VECTORS FOR UNBOUND PARALLEL RT-TRANSITION *****)
+(* STRONGLY NORMALIZING TERM VECTORS FOR EXTENDED PARALLEL RT-TRANSITION ****)
 
 (* Advanced properties ************************************* ****************)
 
 (* Basic_1: was just: sn3_appls_beta *)
-lemma csx_applv_beta (h) (G):
-      ∀p,L,Vs,V,W,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.ⓓ{p}ⓝW.V.T⦄ →
-      â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.â\93\90V.â\93\9b{p}W.Tâ¦\84.
-#h #G #p #L #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
+lemma csx_applv_beta (G) (L):
+      ∀p,Vs,V,W,T. ❪G,L❫ ⊢ ⬈*𝐒 ⒶVs.ⓓ[p]ⓝW.V.T →
+      â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶Vs.â\93\90V.â\93\9b[p]W.T.
+#G #L #p #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
 #V0 #Vs #IHV #V #W #T #H1T
 lapply (csx_fwd_pair_sn … H1T) #HV0
 lapply (csx_fwd_flat_dx … H1T) #H2T
@@ -38,11 +38,11 @@ elim (cpxs_fwd_beta_vector … H) -H #H
 ]
 qed.
 
-lemma csx_applv_delta_drops (h) (G):
-      ∀I,L,K,V1,i. ⇩*[i] L ≘ K.ⓑ{I}V1 →
-      ∀V2. ⇧*[↑i] V1 ≘ V2 →
-      â\88\80Vs. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.V2â¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.#iâ¦\84.
-#h #G #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
+lemma csx_applv_delta_drops (G) (L):
+      ∀I,K,V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
+      ∀V2. ⇧[↑i] V1 ≘ V2 →
+      â\88\80Vs. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶Vs.V2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶Vs.#i.
+#G #L #I #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
 [ /4 width=11 by csx_inv_lifts, csx_lref_pair_drops, drops_isuni_fwd_drop2/
 | #V #Vs #IHV #H1T
   lapply (csx_fwd_pair_sn … H1T) #HV
@@ -57,10 +57,10 @@ lemma csx_applv_delta_drops (h) (G):
 qed.
 
 (* Basic_1: was just: sn3_appls_abbr *)
-lemma csx_applv_theta (h) (G):
-      ∀p,L,V1b,V2b. ⇧*[1] V1b ≘ V2b →
-      â\88\80V,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\93{p}V.â\92¶V2b.Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶V1b.â\93\93{p}V.Tâ¦\84.
-#h #G #p #L #V1b #V2b * -V1b -V2b /2 width=1 by/
+lemma csx_applv_theta (G) (L):
+      ∀p,V1b,V2b. ⇧[1] V1b ≘ V2b →
+      â\88\80V,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\93[p]V.â\92¶V2b.T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶V1b.â\93\93[p]V.T.
+#G #L #p #V1b #V2b * -V1b -V2b /2 width=1 by/
 #V1b #V2b #V1 #V2 #HV12 #H
 generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
 elim H -V1b -V2b /2 width=3 by csx_appl_theta/
@@ -76,10 +76,10 @@ elim (cpxs_fwd_theta_vector … (V2⨮V2b) … H1) -H1 /2 width=1 by liftsv_cons
 qed.
 
 (* Basic_1: was just: sn3_appls_cast *)
-lemma csx_applv_cast (h) (G):
-      ∀L,Vs,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.U⦄ →
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\92¶Vs.â\93\9dU.Tâ¦\84.
-#h #G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
+lemma csx_applv_cast (G) (L):
+      ∀Vs,U. ❪G,L❫ ⊢ ⬈*𝐒 ⒶVs.U →
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶Vs.T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\92¶Vs.â\93\9dU.T.
+#G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
 #V #Vs #IHV #U #H1U #T #H1T
 lapply (csx_fwd_pair_sn … H1U) #HV
 lapply (csx_fwd_flat_dx … H1U) #H2U