Theorem pjpji

Description: Decomposition of a vector into projections. (Contributed by NM, 6-Nov-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	pjpj.1	|- H e. CH
	pjpj.2	|- A e. ~H
Assertion	pjpji	|- A = ( ( ( projh ` H ) ` A ) +h ( ( projh ` ( _|_ ` H ) ) ` A ) )

Proof

Step	Hyp	Ref	Expression
1		pjpj.1	|- H e. CH
2		pjpj.2	|- A e. ~H
3	1 2	pjpj0i	|- A = ( ( ( projh ` H ) ` A ) +h ( ( projh ` ( _|_ ` H ) ) ` A ) )