Restructuring Initiatives (Schedule of restructuring charges) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 27, 2016	Nov. 29, 2015	Nov. 27, 2016	Nov. 29, 2015
Restructuring and Related Cost [Line Items]
Severance	$ 15.5	$ 28.0	$ 30.5	$ 75.4
Asset write-offs	7.2	10.1	43.9	12.5
Accelerated depreciation	12.8	21.2	29.2	42.6
Other	6.3	23.8	10.7	34.5
Total restructuring charges	41.8	83.1	114.3	165.0
Closure of Melbourne, Australia plant [Member]
Restructuring and Related Cost [Line Items]
Severance	11.3	0.0	11.3	0.0
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation	0.7	0.0	0.7	0.0
Other	0.0	0.0	0.0	0.0
Total restructuring charges	12.0	0.0	12.0	0.0
Restructuring of Certain International Product Lines [Member]
Restructuring and Related Cost [Line Items]
Severance	4.1	0.0	6.4	0.0
Asset write-offs	2.2	0.0	35.8	0.0
Accelerated depreciation		0.0		0.0
Accelerated depreciation reversal	(0.3)		(0.3)
Other	0.9	0.0	1.4	0.0
Total restructuring charges	6.9	0.0	43.3	0.0
Closure of Vineland, New Jersey Plant [Member]
Restructuring and Related Cost [Line Items]
Severance		0.0	12.3	0.0
Severance reversal	(0.1)
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation	7.0	0.0	14.0	0.0
Other	0.1	0.0	1.6	0.0
Total restructuring charges	7.0	0.0	27.9	0.0
Project Compass [Member]
Restructuring and Related Cost [Line Items]
Severance	0.0	2.2	0.0	47.1
Asset write-offs	0.0	0.0	0.0	0.0
Accelerated depreciation	0.0	0.0	0.2	0.0
Other	0.0		0.8	6.5
Other reversal		(0.1)
Total restructuring charges	0.0	2.1	1.0	53.6
Project Century [Member]
Restructuring and Related Cost [Line Items]
Severance	0.2	25.8	0.5	28.1
Asset write-offs	5.0	10.1	8.1	12.5
Accelerated depreciation	5.4	21.2	14.6	42.6
Other	5.3	23.9	6.9	28.0
Total restructuring charges	$ 15.9	$ 81.0	30.1	111.2
Project Catalyst [Member]
Restructuring and Related Cost [Line Items]
Severance			0.0	0.2
Asset write-offs			0.0	0.0
Accelerated depreciation			0.0	0.0
Other			0.0	0.0
Total restructuring charges			$ 0.0	$ 0.2