Corollary 1
Tag 07X5, permanent. Cite it as [Bourbaki, Tag 07X5].
Topological Vector Spaces, chapter V, § 1. Prehilbertian spaces and hilbertian spaces
— If f is a positive hermitian form, the set N of all x \in E such that f(x, x) = 0 coincides with the vector subspace of all x \in E such that f(x, y) = 0 for all y \in E.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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