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I am referring to this paper by S. K. Donaldson. I could not find a freely available version, hence I feel uncomfortable to copy & paste parts of his paper, and won't do so. Nevertheless, I will have to reference it.

I am trying to understand the proof of part a.) of his sole Lemma (p.129). I'm fine up to and including the very last equality concerning $\Gamma_{dH}$ at the bottom of p.129. What I do not see is how pulling back this term gives the equality of definitions.

I would be very grateful if somebody could explain this to me.

Thank you.

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