Theorem hilhl

Description: The Hilbert space of the Hilbert Space Explorer is a complex Hilbert space. (Contributed by Steve Rodriguez, 29-Apr-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	hilhl	$$⊢⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩\in {CHil}_{\mathrm{OLD}}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩=⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩$$
2	1	hhhl	$$⊢⟨⟨{+}_{ℎ},{\cdot }_{ℎ}⟩,{norm}_{ℎ}⟩\in {CHil}_{\mathrm{OLD}}$$