induction n; induction m; auto with algebra; intros.
inversion_clear H.
inversion_clear H.
simpl in |- *.
apply IHn; auto with algebra.
simpl in |- *; simpl in H; auto with arith.
Qed.

Lemma Kronecker_case_unequal :
forall (A : Setoid) (t f : A) (n m : Nat),
~ n =' m in _ -> Kronecker t f n m =' f in _.