Discrete dividends, law of one price

(a) Prove Prop. 7.2, $F_0 = (S_0 - I)e^{rT}$, by the law of one price: construct two portfolios with the same payoff at $T$ and no intermediate net cash flows, one containing the forward. (b) A stock pays a single dividend $D$ at $t_1 < T$. Suppose that on the ex-date the stock price drops by exactly $D$. Show that the forward price for delivery at $T$ is continuous across the ex-date. What happens to the forward price if the stock drops by less than $D$, and what does this say about trading futures around ex-dates?