universary milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / grammar / term_vector.ma

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 9575612e0d881fa9bd67a38534126178d7169c5a..d33d4b452e6dbae33e9c5e2db29fa2a4bc31cd75 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/term_vector.ma
@@ -18,7 +18,7 @@ include "basic_2/grammar/term_simple.ma".
 
 (* TERMS ********************************************************************)
 
-let rec applv Vs T on Vs ≝
+rec definition applv Vs T on Vs ≝
   match Vs with
   [ nil        ⇒ T
   | cons hd tl ⇒ ⓐhd. (applv tl T)
@@ -27,8 +27,16 @@ let rec applv Vs T on Vs ≝
 interpretation "application to vector (term)"
    'SnApplVector Vs T = (applv Vs T).
 
-(* properties concerning simple terms ***************************************)
+(* Basic properties *********************************************************)
 
-lemma applv_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.