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The cold girl probably had enlightment and the author didn't really tell what happened to the cold girl after the exchange battle.. seeing that she was determined to join where Kim Seojoon is, she might've abandoned the mentality that "she was better than everyone". Also, in a few panels we could see Lee Hayeon's expression go dark, so to say, she did went through something after the exchange battle. （￣へ￣）
I think in future chapters we could see Lee Hayeon's backstory about what happened after the exchange battle. ╮(￣▽￣)╭