The proof of #2 is encryption exists. You can build a CSPRNG out of a cipher that's secure against chosen plaintext attack (trivial construction: encrypt a coun

The proof of #2 is encryption exists. You can build a CSPRNG out of a cipher that's secure against chosen plaintext attack (trivial construction: encrypt a counter with your seed key). We haven't necessarily proven that encryption exists in the fully theoretical sense, but if you're considering the possibility that CSPRNGs don't exist, that means you have to simultaneously consider that encryption itself isn't meaningfully possible.