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Stock Plans (Schedule of information on stock option activity) (Details)
$ / shares in Units, $ in Millions
9 Months Ended
Feb. 25, 2018
USD ($)
$ / shares
shares
Options Outstanding [Abstract]  
Beginning Balance, Outstanding | shares 29,834,400
Granted | shares 2,816,700
Exercised | shares (3,207,200)
Forfeited or expired | shares (146,800)
Ending Balance, Outstanding | shares 29,297,100
Ending Balance, Exercisable | shares 20,297,200
Weighted Average Exercise Price Per Share [Abstract]  
Beginning Balance, Outstanding | $ / shares $ 40.47
Granted | $ / shares 55.52
Exercised | $ / shares 31.43
Forfeited or expired | $ / shares 58.69
Ending Balance, Outstanding | $ / shares 42.82
Ending Balance, Exercisable | $ / shares $ 36.08
Weighted Average Remaining Contractual Term [Abstract]  
Ending Balance, Outstanding 4 years 4 months 10 days
Ending Balance, Exercisable 2 years 8 months 26 days
Aggregate Intrinsic Value [Abstract]  
Ending Balance, Outstanding | $ $ 343.4
Ending Balance, Exercisable | $ $ 343.4