Notation "∑" := (msum plus 0).

(* Specifications: *)
Lemma dio_rel_binomial b n k : 𝔻P b -> 𝔻P n -> 𝔻P k -> 𝔻R (fun ν => b ν = binomial (n ν) (k ν)).
Lemma rel_iter_iter_bound n x y : rel_iter R n x y -> rel_iter_bound n x y.
Theorem rel_iter_bound_equiv n x y : rel_iter R n x y <-> rel_iter_bound n x y.