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I have a question regarding a proof. The proof uses some results I first present:

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My question is regarding the proof in the last point which is here:

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But how does the last sentence follow, is it easy? How can we just pair up coefficients, what makes them vanish when $k \ne l$. And why must a coefficient with a given k on the l.h.s. correspond to the same k on the r.h.s?

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    Power series are unique. – 2017-01-07
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    The first sum runs over general exponents $(k, l)$ of $s$ and $t$ respectively. The second sum runs over exponents of the form $(k,k)$ only. This is why the coefficients vanish for $k \neq l$ – 2017-01-07

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