intros m; case m; simpl; auto.
intros H'; inversion H'; auto.
intros m; case m; simpl; auto.
intros H'0; contradict H'0; auto with arith.
intros n1 H'0; rewrite !IH; auto with arith.
Qed.

Lemma bin_nn: forall (n : nat),  bin n n = 1.
intros n; induction n as [| n IH]; intros; simpl; auto.