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to have met you语法跟用法都是没有错的.
可以跟meeting you互换.
至于meeting you的语法大概是口语上的一种省略.
当俩人在非正式场合初次见面时,现在已经很少有人用"How do you do?"来互相问候了,取而代之的便是"Nice to meet you."或"Nice to know you.",人们还习惯用"Nice to see you."来表示问候.分别时则常说"Nice seeing you.","Nice talking with you.","Nice to have met you."或"Nice meeting you."等.
楼上的"用现在分词表示过去已经发生了的事情"这句结论确实高..