- predefined_virtuals: some additions

[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 00de73f528cc89cf85672740d583628754ac7439..205642fac210cb13bfcf95d8de7081302b716343 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
@@ -22,17 +22,15 @@ 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] → 
+lemma csn_applv_cnf: ∀L,T. 𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ → 
                      ∀Vs. L ⊢ ⬇* Vs → L ⊢ ⬇* Ⓐ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
 @csn_appl_simple_tstc // -HV /2 width=1/ -IHV -HVs
-[ #X #H #H0
-  lapply (cprs_fwd_cnf_vector … H) -H // -H1T -H2T #H
-  elim (H0 ?) -H0 //
-| -L -V elim Vs -Vs //
-]
+#X #H #H0
+lapply (cprs_fwd_cnf_vector … H) -H // -H1T -H2T #H
+elim (H0 ?) -H0 //
 qed.
 
 (* Basic_1: was: sn3_appls_beta *)
@@ -44,12 +42,10 @@ lemma csn_applv_beta: ∀L,W. L ⊢ ⬇* W →
 lapply (csn_fwd_pair_sn … H1T) #HV0
 lapply (csn_fwd_flat_dx … H1T) #H2T
 @csn_appl_simple_tstc // -HV0 /2 width=1/ -IHV -H2T
-[ #X #H #H0
-  elim (cprs_fwd_beta_vector … H) -H #H
-  [ -H1T elim (H0 ?) -H0 //
-  | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-  ]
-| -H1T elim Vs -Vs //
+#X #H #H0
+elim (cprs_fwd_beta_vector … H) -H #H
+[ -H1T elim (H0 ?) -H0 //
+| -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
 ]
 qed.
 
@@ -64,12 +60,10 @@ lemma csn_applv_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
   lapply (csn_fwd_pair_sn … H1T) #HV
   lapply (csn_fwd_flat_dx … H1T) #H2T
   @csn_appl_simple_tstc // -HV /2 width=1/ -IHV -H2T
-  [ #X #H #H0
-    elim (cprs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
-    [ -H1T elim (H0 ?) -H0 //
-    | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-    ]
-  | -L -K -V -V1 -V2 elim Vs -Vs //
+  #X #H #H0
+  elim (cprs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
+  [ -H1T elim (H0 ?) -H0 //
+  | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
   ]
 ]
 qed.
@@ -87,7 +81,7 @@ 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/
 ]
@@ -96,18 +90,16 @@ qed.
 (* Basic_1: was: sn3_appls_cast *)
 lemma csn_applv_tau: ∀L,W. L ⊢ ⬇* W →
                      ∀Vs,T. L ⊢ ⬇* ⒶVs. T →
-                     L â\8a¢ â¬\87* â\92¶Vs. â\93£W. T.
+                     L â\8a¢ â¬\87* 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
 lapply (csn_fwd_flat_dx … H1T) #H2T
 @csn_appl_simple_tstc // -HV /2 width=1/ -IHV -H2T
-[ #X #H #H0
-  elim (cprs_fwd_tau_vector … H) -H #H
-  [ -H1T elim (H0 ?) -H0 //
-  | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-  ]
-| -H1T elim Vs -Vs //
+#X #H #H0
+elim (cprs_fwd_tau_vector … H) -H #H
+[ -H1T elim (H0 ?) -H0 //
+| -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
 ]
 qed.