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Revenue from Contracts with Customers Revenue Disaggregated By Contract Type (Details) - USD ($)
$ in Millions
12 Months Ended
Jun. 01, 2019
Jun. 02, 2018
Jun. 03, 2017
Disaggregation of Revenue [Line Items]      
Net sales $ 2,567.2 $ 2,381.2 $ 2,278.2
Single performance obligation | Product revenue      
Disaggregation of Revenue [Line Items]      
Net sales 2,155.0    
Multiple performance obligations | Product revenue      
Disaggregation of Revenue [Line Items]      
Net sales 390.0    
Multiple performance obligations | Service revenue      
Disaggregation of Revenue [Line Items]      
Net sales 12.6    
Other      
Disaggregation of Revenue [Line Items]      
Net sales $ 9.6