Definition pick (l: ne_list.L X): MonoidMonadTrans.M m ne_tree_monad.ext X
    := lift (MonoidMonadTrans.T m) ne_tree_monad.ext X (ne_tree_monad.pick l).

Lemma In_pick_inv (l: ne_list.L X) (r: prod m X): ne_tree.In r (pick l) -> fst r = monoid_zero m /\ In (snd r) l.