Restructuring Initiatives (Schedule of restructuring charges classification) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 25, 2018	Feb. 26, 2017	Feb. 25, 2018	Feb. 26, 2017
Restructuring and Related Cost [Line Items]
Total charges	$ 7.6	$ 94.0	$ 27.3	$ 208.3
Project-related costs classified in cost of sales	3.0	11.5	8.4	36.4
Cost of Sales [Member]
Restructuring and Related Cost [Line Items]
Total charges	0.1	16.4	13.0	42.8
Restructuring, Impairment, and Other Exit Costs [Member]
Restructuring and Related Cost [Line Items]
Total charges	$ 7.5	$ 77.6	$ 14.3	$ 165.5