Definition M: Monad := MonoidMonadTrans.M NatAddMonoid ne_tree_monad.ext.Definition cmp (x y: E): M comparison :=
    @ret ne_tree_monad.M _ (1%nat, sort_order.Ecmp E x y).Definition pick := monoid_tree_monad.pick NatAddMonoid.

Lemma partition d l: partition M cmp d l = ne_tree.Leaf (length l, qs_definitions.simplerPartition E d l).