Theorem hhims2

Description: Hilbert space distance metric. (Contributed by NM, 10-Apr-2008) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hhnv.1	|- U = <. <. +h , .h >. , normh >.
	hhims2.2	|- D = ( IndMet ` U )
Assertion	hhims2	|- D = ( normh o. -h )

Proof

Step	Hyp	Ref	Expression
1		hhnv.1	|- U = <. <. +h , .h >. , normh >.
2		hhims2.2	|- D = ( IndMet ` U )
3		eqid	|- ( normh o. -h ) = ( normh o. -h )
4	1 3	hhims	|- ( normh o. -h ) = ( IndMet ` U )
5	2 4	eqtr4i	|- D = ( normh o. -h )