Proof with auto.
unfold monoid_expec_sum.
intros.
intro.
unfold compose.
f_equal.
apply map_ext.
intro.
f_equal.
apply H.
Qed.

Lemma monoid_expec_Node_map (A B: Set) (f: A -> MonoidMonadTrans.M m ne_tree_monad.ext B) (l: ne_list.L A):
monoid_expec (ne_tree.Node (ne_list.map f l)) =
monoid_expec_sum f l / INR (length l).