Proof with auto. (* todo: rename *)
induction l...
simpl.
rewrite (@mon_assoc (ne_tree_monad.M)).
rewrite IHl.
simpl.
rewrite app_nil_r...
Qed.

Lemma simplePartition_component (ee: E) i cr l:
proj1_sig (simplerPartition ee i l) cr =
filter (fun f => unsum_bool (cmp_cmp (Ecmp ee f i) cr)) l.