Hi, I have a question on the proof of theorem 2.4.

Theorem 2.4 If P and ! are riskless zero-coupon bonds with the same maturity time T, then they are of equal value at all previous times.

Proof: Suppose both bonds P and Q are guarranteed to be worth exactly 1 pound at time T. then Q is worth as much as P in all possible worlds at time T, so Q is worth at least as much as P in all possible worlds at all previous times. By symmetry, we conclude that P is also worth as much as Q., and thus P and Q have the same price in all possible worlds at all times.

I don't understand the sentence highlighted in red. Why must Q be worth as much as P in all possible worlds at time T? Can't Q be worth as much as P in some world states and P be worth as much as Q in some world state? just like in theorem 2.5?

Theorem 2.4 is a stronger assumption then theorem 2.5, Theorems 2.5 states that P is stronger than Q in some state and Q is stronger than P in some state.