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[D] InfoGAN loss derivation confusion

I’m a bit confused by the derivation of a lemma in the appendix of the InfoGAN paper (Appendix A lemma). I have added the link to the paper here (https://arxiv.org/abs/1606.03657)

In particular, between third and fourth line, f(x,y) turns into f(x’,y). How does that work?

submitted by /u/mellow54
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