unfold ijs.
simpl.
intros.
destruct (In_concat_inv _ _ H). clear H.
destruct H0.
destruct (In_map_inv H0). clear H0.
destruct H1.
subst.
destruct (In_map_inv H). clear H.
destruct H0.
inversion H.
subst.
split.
destruct (In_nats_inv _ _ _ H0)...
destruct (In_nats_inv _ _ _ H1)...
Qed.

(* Specifications: *)
Lemma expand_sumOver_ijs n (f: nat * nat -> R):
RsumOver (ijs n) f =
RsumOver (nats 0 n) (fun j => RsumOver (nats 0 j) (fun i => f (i, j))).