(A : Type) (n : nat) (f : forall (i : nat), (i < n)%nat -> A) : Vector A n. Proof. exists (list_map (fun '(i; Hi) => f i Hi) (seq' n)). lhs nrapply length_list_map. apply length_seq'. Defined.
Require Import Basics.Overture Basics.Trunc Basics.Tactics Basics.PathGroupoids. Require Import Types.Sigma. Require Import Algebra.AbGroups.AbelianGroup Algebra.Rings.Ring Algebra.Rings.Module. Require Import Spaces.Nat.Core. Require Import Spaces.List.Core Spaces.List.Theory Spaces.List.Paths. Require Import abstract_algebra.