First, note that under the assumption that there are no arbitrage opportunities (the prices are arbitrage-free), two portfolios that always have the same payoff at time T must have the same value at any prior time. To prove this suppose that, at some time "t" before "T", one portfolio were cheaper than the other. Then one could purchase (go long) the cheaper portfolio and sell (go short) the more expensive. At time "T", our overall portfolio would, for any value of the share price, have zero value (all the assets and liabilities have canceled out). The profit we made at time "t" is thus a riskless profit, but this violates our assumption of no arbitrage.