Proof with auto.
unfold monoid_expec, monoid_expec_sum.
intros.
rewrite expec_Node.
rewrite ne_list.map_map.
unfold Ravg.
rewrite ne_list.map_length.
unfold monoid_expec.
rewrite ne_list.plain_map...
Qed.

Lemma monoid_expec_ret (A: Set) (a: A): monoid_expec (ret a) = 0.
Proof with auto.