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Stock Plans (Schedule of information on stock option activity) (Details)
$ / shares in Units, $ in Millions
6 Months Ended
Nov. 27, 2016
USD ($)
$ / shares
shares
Options Outstanding [Abstract]  
Beginning Balance, Outstanding | shares 32,401,600
Granted | shares 2,446,000
Exercised | shares (3,302,900)
Forfeited or expired | shares (62,400)
Ending Balance, Outstanding | shares 31,482,300
Ending Balance, Exercisable | shares 22,465,800
Weighted Average Exercise Price Per Share [Abstract]  
Beginning Balance, Outstanding | $ / shares $ 37.09
Granted | $ / shares 66.52
Exercised | $ / shares 30.37
Forfeited or expired | $ / shares 58.48
Ending Balance, Outstanding | $ / shares 40.04
Ending Balance, Exercisable | $ / shares $ 33.63
Weighted Average Remaining Contractual Term [Abstract]  
Ending Balance, Outstanding 4 years 6 months 25 days
Ending Balance, Exercisable 3 years 1 month 24 days
Aggregate Intrinsic Value [Abstract]  
Ending Balance, Outstanding | $ $ 710.9
Ending Balance, Exercisable | $ $ 644.0