Definition normalize {X} `{Finite X} (d : dist X) : dist X.

Lemma list_sum_remove_aux_map {X} `{EqDec X} (a : X) : forall (l : list X) (f : X -> nat), In a l -> (list_sum (map f (remove_aux Classes.eqb l a)) = list_sum (remove_aux Nat.eqb (map f l) (f a)))%nat.