Theorem ressip

Description: The inner product is unaffected by restriction. (Contributed by Thierry Arnoux, 16-Jun-2019)

	Ref	Expression
Hypotheses	resssca.1	|- H = ( G |`s A )
	ressip.2	|- ., = ( .i ` G )
Assertion	ressip	|- ( A e. V -> ., = ( .i ` H ) )

Proof

Step	Hyp	Ref	Expression
1		resssca.1	|- H = ( G |`s A )
2		ressip.2	|- ., = ( .i ` G )
3		df-ip	|- .i = Slot 8
4		8nn	|- 8 e. NN
5		1lt8	|- 1 < 8
6	1 2 3 4 5	resslem	|- ( A e. V -> ., = ( .i ` H ) )