What proves this?
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By the time Tom clues in, Daisy and Gatsby are trying to hold back on the public affection. Gatsby, Jordan, Nick, Tom, and Daisy are lunching at Tom and Daisy's mansion. They discuss going into town and Tom notices the passionate gaze Gatsby gives towards his wife. Things really fall apart when Tom receives confirmation of his suspicions. Later that day in a hotel room, in front of pretty much everyone, Gatsby declares to Tom that he and Daisy are in fact in love and that Daisy never really loved him in the first place. Ouch!
The exact point when Tom realises is when Daisy says 'you always look so cool' to Gatsby