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Stock Plans (Schedule of information on stock option activity) (Details)
$ / shares in Units, $ in Millions
9 Months Ended
Feb. 26, 2017
USD ($)
$ / shares
shares
Options Outstanding [Abstract]  
Beginning Balance, Outstanding | shares 32,401,600
Granted | shares 2,446,000
Exercised | shares (3,980,200)
Forfeited or expired | shares (103,900)
Ending Balance, Outstanding | shares 30,763,500
Ending Balance, Exercisable | shares 21,816,900
Weighted Average Exercise Price Per Share [Abstract]  
Beginning Balance, Outstanding | $ / shares $ 37.09
Granted | $ / shares 66.52
Exercised | $ / shares 30.43
Forfeited or expired | $ / shares 57.44
Ending Balance, Outstanding | $ / shares 40.22
Ending Balance, Exercisable | $ / shares $ 33.75
Weighted Average Remaining Contractual Term [Abstract]  
Ending Balance, Outstanding 4 years 4 months 13 days
Ending Balance, Exercisable 2 years 11 months 16 days
Aggregate Intrinsic Value [Abstract]  
Ending Balance, Outstanding | $ $ 662.9
Ending Balance, Exercisable | $ $ 602.6