Definition alt_perms l: list (list T) :=
    match l with
    | nil => nil :: nil
    | _ => concat (map (fun p => (map (cons (fst p)) (perms (snd p)))) (splits l))
    end.

Lemma splits_permuted (l l': list T): Permutation l l' -> Permuted (fun x y => fst x = fst y /\ Permutation (snd x) (snd y)) (splits l) (splits l').