Example 1
Tag 07XH, permanent. Cite it as [Bourbaki, Tag 07XH].
Topological Vector Spaces, chapter V, § 1. Prehilbertian spaces and hilbertian spaces
The prehilbertian spaces defined in examples 1, 3, 4 of V, p. 4, are hilbertian spaces. On the other hand, the prehilbertian space defined in example 2 is neither Hausdorff, nor complete. The complexification of a hilbertian space is a hilbertian space.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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