Theorem hladdf

Description: Mapping for Hilbert space vector addition. (Contributed by NM, 7-Sep-2007) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hladdf.1	⊢ 𝑋 = ( BaseSet ‘ 𝑈 )
	hladdf.2	⊢ 𝐺 = ( +𝑣 ‘ 𝑈 )
Assertion	hladdf	⊢ ( 𝑈 ∈ CHilOLD → 𝐺 : ( 𝑋 × 𝑋 ) ⟶ 𝑋 )

Proof

Step	Hyp	Ref	Expression
1		hladdf.1	⊢ 𝑋 = ( BaseSet ‘ 𝑈 )
2		hladdf.2	⊢ 𝐺 = ( +𝑣 ‘ 𝑈 )
3		hlnv	⊢ ( 𝑈 ∈ CHilOLD → 𝑈 ∈ NrmCVec )
4	1 2	nvgf	⊢ ( 𝑈 ∈ NrmCVec → 𝐺 : ( 𝑋 × 𝑋 ) ⟶ 𝑋 )
5	3 4	syl	⊢ ( 𝑈 ∈ CHilOLD → 𝐺 : ( 𝑋 × 𝑋 ) ⟶ 𝑋 )