They are just about equally natural to me. Personally, I would add the preposition for before winning in #1.
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Thomas TompionDon't you think that adding a preposition would run the danger of making the 'in winning' or 'at winning' refer back to the subject 'we'?No, not at all.
Thomas Tompionthe gerund can easily sound very formal.The first sentence doesn’t strike me as particularly formal at all. I’d say both are styli
Thomas TompionWe are extremely proud of her in winning a gold medal at the Olympics. In winning a gold medal at the Olympics we are extremely proud of her.Neither of those are correct.
Thomas Tompionthe famous issue of in + verb-ing forms referring naturally to the subject.Well, in We are extremely proud of her
Aspara Gus Thomas TompionWe are extremely proud of her in winning a gold medal at the Olympics. In winning a gold medal at the Olympics we are extremely proud of her.Neither of those are correct.Thomas Tompionthe famous issue of in + verb-ing forms referring naturally to the subject.Well, in We are extremely proud of her for winning a gold medal at the Olympics, the only n
Thomas TompionWe seem to agree that most propositions don't work in this case, but that for is permissible.But for different reasons, I think. You seem to be saying that other prepositions don’t work for semantic reasons, while I’m saying that they’re simply not grammatical. That is, it’s not because I interpret the subject of winning as we that
Thomas TompionBut you'd agree, wouldn't you, that by winning and in winning and on winning, for instance, would naturally refer to the subject of the sentence?I still interpret the subject as her (even though all of those preps sound wrong). They all seem like non-native versions of We are extremely proud of her for winning a gold medal at th