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 054fb100baa227c62cf8ade0cc530cd5311bd35c..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
@@ -12,25 +12,25 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/cpxs_theq_vector.ma".
-include "basic_2/rt_computation/csx_simple_theq.ma".
+include "basic_2/rt_computation/cpxs_teqo_vector.ma".
+include "basic_2/rt_computation/csx_simple_teqo.ma".
 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
-@csx_appl_simple_theq /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
+@csx_appl_simple_teqo /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
 #X #H #H0
 elim (cpxs_fwd_beta_vector … H) -H #H
 [ -H1T elim H0 -H0 //
@@ -38,16 +38,16 @@ 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 →
-      â\88\80V2. â¬\86*[↑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 →
+      â\88\80V2. â\87§[↑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
   lapply (csx_fwd_flat_dx … H1T) #H2T
-  @csx_appl_simple_theq /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
+  @csx_appl_simple_teqo /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
   #X #H #H0
   elim (cpxs_fwd_delta_drops_vector … HLK … HV12 … H) -HLK -HV12 -H #H
   [ -H1T elim H0 -H0 //
@@ -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/
@@ -68,7 +68,7 @@ elim H -V1b -V2b /2 width=3 by csx_appl_theta/
 lapply (csx_appl_theta … H … HW12) -H -HW12 #H
 lapply (csx_fwd_pair_sn … H) #HW1
 lapply (csx_fwd_flat_dx … H) #H1
-@csx_appl_simple_theq /2 width=3 by simple_flat/ -IHV12b -HW1 -H1 #X #H1 #H2
+@csx_appl_simple_teqo /2 width=3 by simple_flat/ -IHV12b -HW1 -H1 #X #H1 #H2
 elim (cpxs_fwd_theta_vector … (V2⨮V2b) … H1) -H1 /2 width=1 by liftsv_cons/ -HV12b -HV12
 [ -H #H elim H2 -H2 //
 | -H2 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
@@ -76,15 +76,15 @@ 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
 lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_theq /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2U -H2T
+@csx_appl_simple_teqo /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2U -H2T
 #X #H #H0
 elim (cpxs_fwd_cast_vector … H) -H #H
 [ -H1U -H1T elim H0 -H0 //