From Undecidability.Shared.Libs.PSL Require Import BasicDefinitions.
From Undecidability.Shared.Libs.PSL Require Import FiniteTypes.FinTypes.
From Undecidability.Shared.Libs.PSL Require Import Vectors.Vectors.
From Undecidability.Shared.Libs.PSL Require Import Vectors.VectorDupfree.
From Undecidability.Shared.Libs.PSL Require Import FiniteTypes.Cardinality.
Definition Fin_initVect (n : nat) : Vector.t (Fin.t n) n :=
tabulate (fun i : Fin.t n => i).

Lemma Fin_initVect_full n k :
Vector.In k (Fin_initVect n).