Is the one in red supposed to be the proof of the Pricing Principle 1? Or merely an intuitive explanation?
If proof, is this rigorous? Or does its proof not need to be rigorous since it is merely a Principle (In this case, I guess I am assuming Principle is synonymous with something like Rule of Thumb)?
If explanation, how does one then prove Pricing Principle 1? Does it follow from Prop 2.9? If so, how does one say this exactly? The fact that other prices besides $\Pi(0;X) = V_0^h$ implies arbitrage possibility means that the fair/reasonable price of $X$ is $\Pi(0;X) = V_0^h$? It seems weird since most math textbooks usually prove statements using previous statements rather than latter ones.