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Commitments and Contingencies - Schedule of Product Warranty Liability (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 26, 2022	Feb. 27, 2021	Feb. 26, 2022	Feb. 27, 2021
Movement in Standard Product Warranty Accrual [Roll Forward]
Accrual Balance — beginning	$ 69.9	$ 59.9	$ 60.1	$ 59.2
Accrual for warranty matters	2.8	2.5	12.0	8.5
Settlements and adjustments	(3.8)	(3.3)	(13.3)	(8.6)
Acquired through business acquisition	0.0	0.0	15.1	0.0
Accrual Balance — ending	73.9	59.1	73.9	59.1
Revision of Prior Period, Adjustment
Movement in Standard Product Warranty Accrual [Roll Forward]
Accrual Balance — beginning	$ 5.0	$ 0.0	$ 0.0	$ 0.0

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

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- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable for estimated claims under standard and extended warranty protection rights granted to customers.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.15(5))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=123368208&loc=d3e12565-110249

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (c)(5)
-URI http://asc.fasb.org/extlink&oid=123368208&loc=d3e12565-110249

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- Definition

Amount of increase in the standard and extended product warranty accrual from a business acquisition.

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Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
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- Definition

Amount of decrease in the standard and extended product warranty accrual from payments made in cash or in kind to satisfy claims under the terms of the standard and extended product warranty.

+ References

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 460
-SubTopic 10
-Section 50
-Paragraph 8
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- Definition

Amount of increase in the standard and extended product warranty accrual from warranties issued.

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-Name Accounting Standards Codification
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