- we introduced the pointer_step rc in the perspective of proving

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / csn_tstc_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_tstc_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_tstc_vector.ma
index 3aa7170f50da7ca220c06e2c529fa290cf4636b6..cfee668b9ed5988cd440b98584092f27af6b43da 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_tstc_vector.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_tstc_vector.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/computation/acp_cr.ma".
 include "basic_2/computation/cprs_tstc_vector.ma".
-include "basic_2/computation/csn_lcpr.ma".
+include "basic_2/computation/csn_lfpr.ma".
 include "basic_2/computation/csn_vector.ma".
 
 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERM VECTORS **********************)
@@ -22,8 +22,8 @@ include "basic_2/computation/csn_vector.ma".
 (* Advanced properties ******************************************************)
 
 (* Basic_1: was only: sn3_appls_lref *)
-lemma csn_applv_cnf: ∀L,T. 𝐒[T] → L ⊢ 𝐍[T] → 
-                     â\88\80Vs. L â\8a¢ â¬\87* Vs â\86\92 L â\8a¢ â¬\87* ⒶVs.T.
+lemma csn_applv_cnf: ∀L,T. 𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ → 
+                     â\88\80Vs. L â\8a¢ â¬\8a* Vs â\86\92 L â\8a¢ â¬\8a* ⒶVs.T.
 #L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(csn_cnf … H2T) ] (**) (* /2 width=1/ does not work *)
 #V #Vs #IHV #H
 elim (csnv_inv_cons … H) -H #HV #HVs
@@ -34,10 +34,10 @@ elim (H0 ?) -H0 //
 qed.
 
 (* Basic_1: was: sn3_appls_beta *)
-lemma csn_applv_beta: ∀L,W. L ⊢ ⬇* W →
-                      â\88\80Vs,V,T. L â\8a¢ â¬\87* â\92¶Vs.â\93\93V.T →
-                      L â\8a¢ â¬\87* â\92¶Vs. â\93\90V.â\93\9bW. T.
-#L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
+lemma csn_applv_beta: ∀a,L,W. L ⊢ ⬊* W →
+                      â\88\80Vs,V,T. L â\8a¢ â¬\8a* â\92¶Vs.â\93\93{a}V.T →
+                      L â\8a¢ â¬\8a* â\92¶Vs. â\93\90V.â\93\9b{a}W. T.
+#a #L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
 #V0 #Vs #IHV #V #T #H1T
 lapply (csn_fwd_pair_sn … H1T) #HV0
 lapply (csn_fwd_flat_dx … H1T) #H2T
@@ -51,7 +51,7 @@ qed.
 
 lemma csn_applv_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
                        ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
-                       â\88\80Vs.L â\8a¢ â¬\87* (â\92¶Vs. V2) â\86\92 L â\8a¢ â¬\87* (ⒶVs. #i).
+                       â\88\80Vs.L â\8a¢ â¬\8a* (â\92¶Vs. V2) â\86\92 L â\8a¢ â¬\8a* (ⒶVs. #i).
 #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
 [ #H
   lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
@@ -69,10 +69,10 @@ lemma csn_applv_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
 qed.
 
 (* Basic_1: was: sn3_appls_abbr *) 
-lemma csn_applv_theta: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                       â\88\80V,T. L â\8a¢ â¬\87* â\93\93V. â\92¶V2s. T â\86\92 L â\8a¢ â¬\87* V →
-                       L â\8a¢ â¬\87* â\92¶V1s. â\93\93V. T.
-#L #V1s #V2s * -V1s -V2s /2 width=1/
+lemma csn_applv_theta: ∀a,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+                       â\88\80V,T. L â\8a¢ â¬\8a* â\93\93{a}V. â\92¶V2s. T â\86\92 L â\8a¢ â¬\8a* V →
+                       L â\8a¢ â¬\8a* â\92¶V1s. â\93\93{a}V. T.
+#a #L #V1s #V2s * -V1s -V2s /2 width=1/
 #V1s #V2s #V1 #V2 #HV12 #H 
 generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
 elim H -V1s -V2s /2 width=3/
@@ -81,16 +81,16 @@ lapply (csn_appl_theta … HW12 … H) -H -HW12 #H
 lapply (csn_fwd_pair_sn … H) #HW1
 lapply (csn_fwd_flat_dx … H) #H1
 @csn_appl_simple_tstc // -HW1 /2 width=3/ -IHV12s -HV -H1 #X #H1 #H2
-elim (cprs_fwd_theta_vector … (V2::V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
+elim (cprs_fwd_theta_vector … (V2@V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
 [ -H #H elim (H2 ?) -H2 //
 | -H2 #H1 @(csn_cprs_trans … H) -H /2 width=1/
 ]
 qed.
 
 (* Basic_1: was: sn3_appls_cast *)
-lemma csn_applv_tau: â\88\80L,W. L â\8a¢ â¬\87* W →
-                     â\88\80Vs,T. L â\8a¢ â¬\87* ⒶVs. T →
-                     L â\8a¢ â¬\87* â\92¶Vs. â\93£W. T.
+lemma csn_applv_tau: â\88\80L,W. L â\8a¢ â¬\8a* W →
+                     â\88\80Vs,T. L â\8a¢ â¬\8a* ⒶVs. T →
+                     L â\8a¢ â¬\8a* â\92¶Vs. â\93\9dW. T.
 #L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
 #V #Vs #IHV #T #H1T
 lapply (csn_fwd_pair_sn … H1T) #HV
@@ -103,12 +103,12 @@ elim (cprs_fwd_tau_vector … H) -H #H
 ]
 qed.
 
-theorem csn_acr: acr cpr (eq â\80¦) (csn â\80¦) (λL,T. L â\8a¢ â¬\87* T).
+theorem csn_acr: acr cpr (eq â\80¦) (csn â\80¦) (λL,T. L â\8a¢ â¬\8a* T).
 @mk_acr //
 [ /3 width=1/
 | /2 width=1/
 | /2 width=6/
-| #L #V1 #V2 #HV12 #V #T #H #HVT
+| #L #V1 #V2 #HV12 #a #V #T #H #HVT
   @(csn_applv_theta … HV12) -HV12 //
   @(csn_abbr) //
 | /2 width=1/