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Investments in Nonconsolidated Affiliates Investments in Nonconsolidated Affiliates - Schedule of Equity Method Earnings (Details) - USD ($)
$ in Millions
12 Months Ended
Jun. 03, 2017
May 28, 2016
May 30, 2015
Equity Method Investments and Joint Ventures [Abstract]      
Equity earnings from nonconsolidated affiliates, net of tax $ 1.6 $ 0.4 $ 0.1