Definition 4

Tag 07XA, permanent. Cite it as [Bourbaki, Tag 07XA].

Topological Vector Spaces, chapter V, § 1. Prehilbertian spaces and hilbertian spaces

*A prehilbertian space is a set $E$ with the structure of a vector space over $K$ and with a positive hermitian form. We say that $E$ is a real (resp. complex) prehilbertian space when $K$ is $\mathbf{R}$ (resp. $K$ is $\mathbf{C}$ ).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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