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Consolidated Balance Sheets (Parenthetical)
$ in Millions
Dec. 31, 2018
USD ($)
shares
Dec. 31, 2018
€ / shares
Dec. 31, 2017
USD ($)
shares
Dec. 31, 2017
€ / shares
Ordinary shares, par value, in USD per share | € / shares   € 0.01   € 0.01
Ordinary shares, number of shares authorized | shares 1,200,000,000   1,200,000,000  
Total equity | $ $ 12,167.1   $ 13,307.6  
Common Stock        
Shares issued | shares 539,289,665   537,902,426  
Total equity | $ $ 6.0   $ 6.0  
Treasury Stock        
Shares issued | shares 23,490,867   13,695,251  
Total equity | $ $ (999.7)   $ (567.7)