Example 2

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

Topological Vector Spaces, chapter II, § 1. Semi-norms

For every linear form $f$ on E, the function $x \mapsto |f(x)|$ is a semi-norm on E.

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

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