(**************************************************************************)
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.