Investments in Nonconsolidated Affiliates Investments in Nonconsolidated Affiliates - Schedule of Sales/Purchases to/from Nonconsolidated Affiliates (Details) - Equity Method Investee - USD ($) $ in Millions	12 Months Ended
	Jun. 01, 2019	Jun. 02, 2018	Jun. 03, 2017
Schedule of Equity Method Investments
Sales to nonconsolidated affiliates	$ 3.9	$ 4.3	$ 4.0
Purchases from nonconsolidated affiliates	$ 23.0	$ 6.8	$ 4.2