The post says
Let G be an arbitrarily long string of independent 50⁄50 bits.
I believe that, in your example, the bits are not independent (indeed, the first and second bits are always equal), thus it isn’t a counterexample.
Sorry if I misunderstood
G can still be independent bits in the proposed counterexample. The mechanism is just about how Y is constructed from A: A is a sequence of bits, Y is A with either 11′s removed or 00′s removed.
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The post says
I believe that, in your example, the bits are not independent (indeed, the first and second bits are always equal), thus it isn’t a counterexample.
Sorry if I misunderstood
G can still be independent bits in the proposed counterexample. The mechanism is just about how Y is constructed from A: A is a sequence of bits, Y is A with either 11′s removed or 00′s removed.