- some additions and corrections

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_vector.ma
index b4a087a1a7672141360864248d609e9f9f68efec..7c26ef429234e39edae390971089dda75455a69c 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_vector.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_vector.ma
@@ -17,10 +17,8 @@ include "basic_2/computation/csn.ma".
 
 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERM VECTORS **********************)
 
-inductive csnv (L:lenv): predicate (list term) ≝
-| csnv_nil: csnv L ◊
-| csn_cons: ∀Ts,T. L  ⊢ ⬇* T → csnv L Ts → csnv L (T :: Ts)
-.
+definition csnv: lenv → predicate (list term) ≝
+                 λL. all … (csn L).
 
 interpretation
    "context-sensitive strong normalization (term vector)"
@@ -28,23 +26,5 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact csnv_inv_cons_aux: ∀L,Ts. L ⊢ ⬇* Ts → ∀U,Us. Ts = U :: Us →
-                        L ⊢ ⬇* U ∧ L ⊢ ⬇* Us.
-#L #Ts * -Ts
-[ #U #Us #H destruct
-| #Ts #T #HT #HTs #U #Us #H destruct /2 width=1/
-]
-qed.
-
-lemma csnv_inv_cons: ∀L,T,Ts. L ⊢ ⬇* T :: Ts → L ⊢ ⬇* T ∧ L ⊢ ⬇* Ts.
-/2 width=3/ qed-.
-
-include "basic_2/computation/csn_cpr.ma".
-
-lemma csn_fwd_applv: ∀L,T,Vs. L ⊢ ⬇* Ⓐ Vs. T → L ⊢ ⬇* Vs ∧ L ⊢ ⬇* T.
-#L #T #Vs elim Vs -Vs /2 width=1/
-#V #Vs #IHVs #HVs
-lapply (csn_fwd_pair_sn … HVs) #HV
-lapply (csn_fwd_flat_dx … HVs) -HVs #HVs
-elim (IHVs HVs) -IHVs -HVs /3 width=1/
-qed-.
+lemma csnv_inv_cons: ∀L,T,Ts. L ⊢ ⬊* T @ Ts → L ⊢ ⬊* T ∧ L ⊢ ⬊* Ts.
+normalize // qed-.