Corollary
Tag 07L5, permanent. Cite it as [Bourbaki, Tag 07L5].
Topological Vector Spaces, chapter III, § 1. Bornology in a topological vector space
In a locally convex space, the set of points of a Cauchy sequence is bounded. In fact, this set is precompact (GT, II, § 4, No. 2).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.