Definition 1
Tag 07TV, permanent. Cite it as [Bourbaki, Tag 07TV].
Topological Vector Spaces, chapter IV, § 3. Dual of a Fréchet space
— A locally convex space E is said to be semi-barrelled if it satisfies the equivalent conditions of prop. 1.
Every barrelled space is semi-barrelled. This is also true for every bornological space (III, p. 22, prop. 10).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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