Definition map_fst (A B C: Set) (f: A -> B) (p: A * C): B * C := (f (fst p), snd p).

Lemma monoid_expec_sum_ext (T U: Set) (f g: T -> MonoidMonadTrans.M m ne_tree_monad.ext U): ext_eq f g -> ext_eq (monoid_expec_sum f) (monoid_expec_sum g).