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Other Intangible Assets, net
 6 Months Ended
Jun. 30, 2019
Goodwill and Intangible Assets Disclosure [Abstract]  
Other intangible assets, net Other Intangible Assets, net 

The following presents a summary of other intangible assets, net:
 
 
 
June 30, 2019 (unaudited)
 
December 31, 2018
(millions)
Weighted
Average
Life (Years)
 
Acquired
Intangible
Assets,
Gross (1)
 
Accumulated
Amortization
 
Acquired
Intangible
Assets,
Net
 
Acquired
Intangible
Assets,
Gross (1)
 
Accumulated
Amortization
 
Acquired
Intangible
Assets,
Net
Covenant not to compete
4.4
 
$
1.6

 
$
(0.2
)
 
$
1.4

 
$
1.6

 
$
—

 
$
1.6

Trade names and trademarks
4.4
 
5.6

 
(0.7
)
 
4.9

 
6.3

 
(0.7
)
 
5.6

Proprietary know how
5.2
 
10.4

 
(1.0
)
 
9.4

 
11.0

 
(0.8
)
 
10.2

Management contract rights
9.5
 
81.0

 
(34.8
)
 
46.2

 
81.0

 
(32.2
)
 
48.8

Customer relationships
14.4
 
100.4

 
(3.9
)
 
96.5

 
100.4

 
(0.6
)
 
99.8

Acquired intangible assets, net (2)
12.0
 
$
199.0

 
$
(40.6
)
 
$
158.4

 
$
200.3

 
$
(34.3
)
 
$
166.0


(1)  Excludes the original cost and accumulated amortization of fully amortized intangible assets.
(2)  Intangible assets have estimated remaining lives between four and fifteen years.

The table below shows the amortization expense related to intangible assets for the three and six months ended June 30, 2019 and June 30, 2018:
 
Three Months Ended
 
Six Months Ended
(millions) (unaudited)
June 30, 2019
 
June 30, 2018
 
June 30, 2019
 
June 30, 2018
Amortization expense related to other intangible assets included in depreciation and amortization
$
3.8

 
$
1.3

 
$
7.6


$
2.7