Let P(t) be the price of a European put option with maturity T and exercise price E. Let r be the riskless rate of interest. Show that P(t) > e^(-r(T-t)) *E-S(t) is an arbitrage-free bound, by proving the contrapositive: if P(t) < e^(-r(T-t) )*E -S(t), then we can construct an arbitrage portfolio. Describe the portfolio carefully.

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