Definition body (v: list X) :=
    match v with
    | nil => ret nil
    | p :: t => partitionPart p t
    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 toBody (l: list X): qs _ cmp l = body l.