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Fair Value of Financial Instruments Fair Value of Financial Instruments - Schedule of Gain/Loss in Other Comprehensive Income (Details) - USD ($)
$ in Millions
12 Months Ended
Jun. 02, 2018
Jun. 03, 2017
May 28, 2016
Derivative Instruments and Hedging Activities Disclosure [Abstract]      
Interest rate swap $ (7.5) $ (2.1) $ 0.0