rewrite <- (vec.list_round_trip l).
cset (vec.from_list l).
intros.
assert (In (nb_val t) (map nb_val (vec.to_list H))).
apply in_map...
rewrite vec.List_map in H2.
assert (In (nb_val t) (vec.nb_nats b (length l))).
apply Permutation.Permutation_in with (vec.to_list (vec.map (nb_val (n:=length ol)) H))...
apply vec.List_Permutation.
apply (vec_IndexSeq_nats_perm H H0).
rewrite vec.length.
rewrite plus_comm.
apply (vec.In_nb_nats_inv _ _ _ H3).
Qed.
Hint Resolve in_map.

(* Specifications: *)
Lemma IndexSeq_base_lowest_value' (b: Index) l: IndexSeq b l -> forall e, In e l -> @Ele UE b e.
Proof with auto.