Corollary 1
Tag 07C0, permanent. Cite it as [Bourbaki, Tag 07C0].
Topological Vector Spaces, chapter II, § 2. Convex sets
— In a Hausdorff topological vector space the convex envelope of a finite set is compact.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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