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diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma
index b9cc288a6..d33d4b452 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma
@@ -13,22 +13,30 @@
 (**************************************************************************)
 
 include "ground_2/lib/list.ma".
-include "basic_2/notation/functions/snappls_2.ma".
+include "basic_2/notation/functions/snapplvector_2.ma".
 include "basic_2/grammar/term_simple.ma".
 
 (* TERMS ********************************************************************)
 
-let rec appls Vs T on Vs ≝
+rec definition applv Vs T on Vs ≝
   match Vs with
   [ nil        ⇒ T
-  | cons hd tl ⇒ ⓐhd. (appls tl T)
+  | cons hd tl ⇒ ⓐhd. (applv tl T)
   ].
 
 interpretation "application to vector (term)"
-   'SnApplStar Vs T = (appls Vs T).
+   'SnApplVector Vs T = (applv Vs T).
 
-(* properties concerning simple terms ***************************************)
+(* Basic properties *********************************************************)
 
-lemma appls_simple: ∀T,Vs.  𝐒⦃T⦄ → 𝐒⦃ⒶVs.T⦄.
+lemma applv_nil: ∀T. Ⓐ◊.T = T.
+// qed.
+
+lemma applv_cons: ∀V,Vs,T. ⒶV@Vs.T = ⓐV.ⒶVs.T.
+// qed.
+
+(* Properties with simple terms *********************************************)
+
+lemma applv_simple: ∀T,Vs. 𝐒⦃T⦄ → 𝐒⦃ⒶVs.T⦄.
 #T * //
 qed.