Restructuring Initiatives (Schedule of restructuring and other exit cost reserves) (Details) $ in Millions	6 Months Ended
	Nov. 27, 2016 USD ($)
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	$ 76.6
Restructuring charges paid out of reserve, including foreign currency translation	33.4
Restructuring reserve utilized	(41.6)
Restructuring Reserve, Ending Balance	68.4
Severance [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	73.6
Restructuring charges paid out of reserve, including foreign currency translation	31.2
Restructuring reserve utilized	(37.5)
Restructuring Reserve, Ending Balance	67.3
Contract Termination [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	1.5
Restructuring charges paid out of reserve, including foreign currency translation	0.0
Restructuring reserve utilized	(1.7)
Restructuring Reserve, Ending Balance	(0.2)
Other Exit Costs [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	1.5
Restructuring charges paid out of reserve, including foreign currency translation	2.2
Restructuring reserve utilized	(2.4)
Restructuring Reserve, Ending Balance	$ 1.3