Proving a Hash in Another Hash I'm new to cryptography in general, and have this basic question.

Provided  H(x) means a hash of x
and z = H(H(x) + H(y))   

given y or H(y), how do we prove that y or H(y) is a part of z? How do we "split" z into H(x) and H(y) so that we can compare H(y) to our y?

Help is greatly appreciated.
I assume you mean H to be a one-way function. The way you 'prove' that you know half of the input of a one-way function (i.e. y or H(y) for the outer H()) will be to produce the other half of the input (i.e. x or H(x)) and show that H() of the two parts together gives you z.

In general, if your H is a Pseudo-random-function (which any good crypto-hash function is), then ANY possible combination of y and z has an infinite number of xs that will combine in the way you ask.