Are parts of a pseudorandom string also a pseudorandom string?
If you have a stream, $s$, of $n$ bits that is computationally indistinguishable from random, then any truncation of that $n$ bit string must also be indistinguishable from random.

The proof of this is straightforward. If $s$ was computationally indistinguishable from random, but some truncation of $s$ was not then we could distinguish the larger sequence from random by enumerating all possible truncations of $s$ and testing them against the distinguisher.

If the distinguisher identifies that any truncation is not random, then this demonstrates $s$ is not random. It acts as a distinguisher on $s$. Obviously, that is a contradiction.