{A : Type} {n} (f : forall (i : nat), (i < n)%nat -> A) i {Hi : (i < n)%nat} : entry (Build_Vector A n f) i = f i Hi. Proof. snrefine (nth'_list_map _ _ _ (_^ # Hi) _ @ _). 1: nrapply length_seq'. snrapply ap011D. 1: nrapply nth'_seq'. rapply path_ishprop. 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.