Income Taxes (Benefit (Expense) of Income Tax) (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Income Taxes [Line Items]
Current	$ (187.5)	$ (1,135.2)	$ (192.3)
Deferred	(65.5)	(438.1)	(46.6)
Total income tax expense	(253.0)	(1,573.3)	(238.9)
The Netherlands
Income Taxes [Line Items]
Current	0.0	14.2	(16.2)
Deferred	(275.3)	(519.4)	(118.2)
Total	(275.3)	(505.2)	(134.4)
Belgium
Income Taxes [Line Items]
Current	(134.7)	(153.9)	(203.6)
Deferred	3.6	41.6	145.4
Total	(131.1)	(112.3)	(58.2)
U.K.
Income Taxes [Line Items]
Current	(1.5)	(7.2)	(3.3)
Deferred	118.8	32.2	(64.7)
Total	117.3	25.0	(68.0)
U.S.
Income Taxes [Line Items]
Current	(4.1)	(957.5)	47.2
Deferred	81.9	7.6	(32.8)
Total	77.8	(949.9)	14.4
Switzerland
Income Taxes [Line Items]
Current	(27.8)	(16.6)	(2.0)
Deferred	(1.1)	6.2	15.6
Total	(28.9)	(10.4)	13.6
Other
Income Taxes [Line Items]
Current	(19.4)	(14.2)	(14.4)
Deferred	6.6	(6.3)	8.1
Total	$ (12.8)	$ (20.5)	$ (6.3)