Restructuring Initiatives (Schedule of restructuring charges) (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]
Severance (reversal)	$ 0.7	$ 66.3	$ (0.4)	$ 96.8
Asset write-offs	0.7	3.7	15.9	52.6
Accelerated depreciation (reversal)	0.1	16.1	12.8	40.3
Other (reversal)	6.1	7.9	(1.0)	18.6
Restructuring charges (reversal)	7.6	94.0	27.3	208.3
Global reorganization [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	67.4	0.6	67.4
Asset write-offs	0.0	0.0	0.6	0.0
Accelerated depreciation (reversal)	0.0	0.0	0.0	0.0
Other (reversal)	0.0	5.7	0.2	5.7
Restructuring charges (reversal)	0.0	73.1	1.4	73.1
Closure of Melbourne, Australia plant [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	0.0	0.6	11.3
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation (reversal)	0.1	5.6	2.2	6.3
Other (reversal)	3.0	0.1	5.2	0.1
Restructuring charges (reversal)	3.1	5.7	8.0	17.7
Restructuring of certain international product lines [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	0.6	0.0	7.0
Asset write-offs	0.0	1.6	0.0	37.4
Accelerated depreciation (reversal)	0.0	0.0	0.0	(0.3)
Other (reversal)	0.0	0.1	0.0	1.5
Restructuring charges (reversal)	0.0	2.3	0.0	45.6
Closure of Vineland, New Jersey plant [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	0.0	(2.2)	12.3
Asset write-offs	0.0	0.4	8.9	5.4
Accelerated depreciation (reversal)	0.0	7.1	10.6	16.1
Other (reversal)	0.2	0.2	(5.0)	1.8
Restructuring charges (reversal)	0.2	7.7	12.3	35.6
Project Compass [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	(1.4)	(0.2)	(1.4)
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation (reversal)	0.0	0.0	0.0	0.2
Other (reversal)	0.0	0.0	0.0	0.8
Restructuring charges (reversal)	0.0	(1.4)	(0.2)	(0.4)
Project Century [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.0	0.2	0.1	0.7
Asset write-offs	0.7	1.7	6.4	9.8
Accelerated depreciation (reversal)	0.0	3.4	0.0	18.0
Other (reversal)	2.9	1.8	(1.4)	8.7
Restructuring charges (reversal)	3.6	7.1	5.1	37.2
Combination of certain operational facilities [Member]
Restructuring and Related Cost [Line Items]
Severance (reversal)	0.7	(0.5)	0.7	(0.5)
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation (reversal)	0.0	0.0	0.0	0.0
Other (reversal)	0.0	0.0	0.0	0.0
Restructuring charges (reversal)	$ 0.7	$ (0.5)	$ 0.7	$ (0.5)