proposition: Lemma vec_to_list_insert {A n} i x (v : vec A n) : vec_to_list (vinsert i x v) = insert (fin_to_nat i) x (vec_to_list v).
proof: Proof. induction v as [|??? IHv]; inv_fin i; [done|]. simpl. intros. by rewrite IHv. Qed.
imports: stdpp(countable) stdpp(options)