+lemma length_mapi: ∀A,B,l.∀f:nat→A→B.∀i.
+ |mapi ?? f l i| = |l|.
+#A #B #l #f elim l // #a #tl #Hind normalize //
+qed.
+
+let rec make_listi (A:Type[0]) (a:nat→A) (n,i:nat) on n : list A ≝
+match n with
+[ O ⇒ [ ]
+| S m ⇒ a i::(make_listi A a m (S i))
+].
+
+lemma length_make_listi: ∀A,a,n,i.
+ |make_listi A a n i| = n.
+#A #a #n elim n // #m #Hind normalize //
+qed.
+
+definition vec_mapi ≝ λA,B.λf:nat→A→B.λn.λv:Vector A n.λi.
+mk_Vector B n (mapi ?? f v i)
+ (trans_eq … (length_mapi …) (len A n v)).
+
+definition make_veci ≝ λA.λa:nat→A.λn,i.
+mk_Vector A n (make_listi A a n i) (length_make_listi A a n i).
+