Definition body n (v: Vector.t X n) :=
    match v with
    | Vector.nil => ret nil
    | l => selectPivotPart l
    end.Definition raw_body_ext (l: list X) (qs qs': {l': list X | length l' < length l} -> M (list X)):
    (forall x y, proj1_sig x = proj1_sig y -> qs x = qs' y) -> raw_body l qs = raw_body l qs'.

Lemma rect (Q: list X -> M (list X) -> Type): (Q nil (ret nil)) -> (forall n (v: Vector.t X (S n)), (forall y, length y < S n -> Q y (qs cmp pick y)) -> Q v (selectPivotPart v)) -> forall x, Q x (qs cmp pick x).