intros.
destruct x.
destruct y.
destruct (eq_nat_dec n n1).
destruct (eq_nat_dec n0 n2).
subst.
left...
right. intro. inversion H...
right. intro. inversion H...
Qed.
Definition UcmpCmp (x y: nat * nat): bool := unsum_bool (UcmpDec x y).
Definition ijcount (i j: nat): monoid -> nat := count (UcmpCmp (i, j)).

Lemma ijcount_0 i j l: ~ In (i, j) l -> ijcount i j l = 0.
Proof with auto.