Restructuring, Impairment, and Other Exit Costs (Schedule of restructuring and other exit cost reserves) (Details) - USD ($) $ in Millions	12 Months Ended
	May 28, 2017	May 29, 2016	May 31, 2015
Restructuring Reserve [Roll Forward]
Reserve beginning balance	$ 76.6	$ 120.8	$ 3.5
Restructuring charges paid out of reserve, including foreign currency translation	104.0	70.2	185.1
Restructuring reserve utilized	(95.6)	(114.4)	(67.8)
Reserve ending balance	85.0	76.6	120.8
Severance [Member]
Restructuring Reserve [Roll Forward]
Reserve beginning balance	73.6	118.6	3.5
Restructuring charges paid out of reserve, including foreign currency translation	95.0	64.3	176.4
Restructuring reserve utilized	(86.8)	(109.3)	(61.3)
Reserve ending balance	81.8	73.6	118.6
Contract Termination [Member]
Restructuring Reserve [Roll Forward]
Reserve beginning balance	1.5	0.6	0.0
Restructuring charges paid out of reserve, including foreign currency translation	0.9	1.6	0.6
Restructuring reserve utilized	(1.7)	(0.7)	0.0
Reserve ending balance	0.7	1.5	0.6
Other Exit Costs [Member]
Restructuring Reserve [Roll Forward]
Reserve beginning balance	1.5	1.6	0.0
Restructuring charges paid out of reserve, including foreign currency translation	8.1	4.3	8.1
Restructuring reserve utilized	(7.1)	(4.4)	(6.5)
Reserve ending balance	$ 2.5	$ 1.5	$ 1.6