Proof with reflexivity.
revert v.
pattern n, i.
apply natBelow_rect_S.
simpl.
intros.
rewrite (eq_cons v).
simpl.
do 2 rewrite remove_head...
intros.
simpl plus.
cset remove_tail.
simpl plus in *.
rewrite H0.
rewrite H0.
simpl.
rewrite <- H.
rewrite (eq_cons v0).
reflexivity.
Qed.

(* Specifications: *)
Lemma remove_perm (T: Set) n (nb: natBelow (S n)) (v: Vector.t T (S n)):
Permutation (Vector.cons (nth v nb) (remove v nb)) v.