Might depend on your background. For a cryptographer, that property is an obvious consequence of being a stream cipher's keystream. For a Monte Carlo guy, it's

Might depend on your background. For a cryptographer, that property is an obvious consequence of being a stream cipher's keystream. For a Monte Carlo guy, it's not obvious, but close to miraculous. And what everyone needs to know is that it doesn't hold for many (non-CS) PRNG, as apparently poker site operators have found out to their chagrin.